The diver involved in the incident has now revealed that he managed to escape the cage through a hole at the bottom - but that there were two other sharks circling him.
Ming Chan was enjoying the dive at Guadalupe Island when the terrifying incident occurred.
According to the Daily Mail, he said on the Today Show: "I felt his panic...and thought 'Hey, come on buddy, you don't want to come into my cage'.
"I didn't have time to get frightened, but found myself outside the cage."
He said he looked down and saw two other sharks just metres from his feet.
He then immediately went back to the cage after seeing the other shark had managed to free itself.
He added: "I saw there was nothing inside the cage... so crawled back up to the surface."
In the video, one stunned onlooker can heard saying "oh my God" as desperate staff quickly open the top of the cage.
The shark appears to thrash around for several seconds as those watching ask "Is it inside?" and "Is he in the cage?"
Then the fish suddenly emerges from the water, bleeding in several places. It manages to free itself and swims away.
A man then asks "Was there anybody in there?" before it It becomes clear that a Ming was inside as staff then pull him up and out of the water. "Gosh, gee, he's ok," the man says.
Ming was shocked but uninjured and some on the boat cheer and clap.
Shark-diving is a controversial tourist attraction, with some experts claiming that baiting for trips such as this leads to an increase in attacks.
The footage was shot near Guadalupe Island, Mexico, by photographer and adventurer Buck Forester.
He posted it onto his YouTube channel where he usually posts updates about his sons Gabe and Garrett.
He wrote: "This is not our normal type of video."I (their dad) went on a great white shark cave diving trip.
"Great white sharks are awesome and what appears to be an 'attack' on a diving cage is not.
"They are temporarily blinded when they open their mouths, so when the shark went for the tuna bait on the rope it accidentally slammed into the cage.
"They can't swim backwards so it thrust forward through the cage with a diver inside.
"The crew on the boat did an outstanding job doing their best to make sure it had this happy outcome."
"These sharks are amazing creatures to be seen up close!"
World's deadliest animals
World's deadliest animals
Although they might look cumbersome and cute, hippos are actually one of the most feared animals in Africa, and can outrun a human. When a male feels its territory is threatened, or a female thinks her offspring her in danger, these animals can be particularly dangerous. And with huge teeth and mouth that can open four feet wide, it's a good idea to steer clear. Kills: An estimated 100-150 people a year. Deadly technique: Hippos will charge, trample and gore its victims, and have been known to upturn boats and canoes without warning. Lives in: Africa
Many people might not realise that the cape buffalo is one of the most dangerous animals in Africa, and will react with force when it feels threatened. These beasts can weigh up to 1.5 tons and stand at 1.7 metres high; they're so intimidating that even lions don't usually consider them dinner. Cape buffalos will charge, and then gore its victim to death with its impressive horns. Kills: An estimated 200 people a year. Deadly technique: These animals will charge and gore their victims to death with their huge horns. Lives in: Africa
Out of the world's 2,000 species of snake, around 250 are thought to be capable of killing a man. The Asian cobra does not have the deadliest venom, but is believed to be responsible for the biggest portion of the thousands of snakebite deaths every year. In Africa, the black mamba is the largest venomous snake and, during an attack, can strike up to 12 times, each time delivering enough neuro and cardio-toxic venom to kill a dozen men within 1 hour. Kills: An estimated 50-125,000 people a year. Deadly technique: A snake will use its fangs to pierce the skin and inject its paralysing venom. Lives in: Africa, Asia, Australia, North America
Box jellyfish can have up to 60 tentacles as long as 15 feet. And each tentacle contains enough venom to kill 50 humans, making it one of the most venomous marine creatures in the world. If stung, a box jellyfish can kill a man within minutes. Kills: An estimated 100 people a year. Deadly technique: Jellyfish use their tentacles to pump venom and paralyse its prey. Deaths in humans are usually a result of cardiac arrest. Lives in: Northern Australia, Papua New Guinea, Malaysia, Indonesia, the Philippines, Thailand and Vietnam.
Apart from humans, the mosquito is the deadliest creature on the planet. It kills millions of people every year through the spread of diseases like malaria, yellow fever, and dengue fever. Many of the malaria victims are children under the age of five. Kills: Two to three million people a year. Deadly technique: Female mosquitos pierce the skin with serrated mouth parts, and inject a saliva with a thinning agent to liquidise the blood. Lives in: Worldwide, more harmful in Africa, Asia and North America
The great white shark, which can grow up to six metres in length and weigh up to five tons, seems to have the most ferocious reputation. But, while they have been known to attack humans, most of these incidents are thought to be 'test bites', where the animal is deciphering whether he wants to eat you. And, generally, they humans are not on the menu. It is thought the aggressive bull shark is responsible for the most attacks on people. Out of the 360 shark species, only four are known killers: the great white, the bull, tiger, and the oceanic white tip. Kills: An estimated 100 people a year. Deadly technique: Sharks use their razor-sharp teeth to rip chunks out of its victims. Great whites usually take a big single bite, drag their victims into deeper waters, and wait until the prey bleeds to death before they eat it. Lives in: Florida, Australia, Hawaii and South Africa.
The are lots of different species of bear, but the polar, black and grizzly are the deadliest. Native to the Arctic, polar bears could decapitate a human being with one swipe of their massive paws. Bears generally attack when they are hungry, so it's a good idea to keep food away from your camp. Kills: An estimated 5 to 10 people a year. Deadly technique: Bear will use their teeth and claws to maul and trample their victims. Lives in: North America, Canada, North Pole, and Russia.
Crocodiles have been around for 200 million years, and are fearsome predators. The saltwater crocodile, or saltie, is the largest living reptile in the world, and can grow up to 21ft long and weigh 1.6 tons. These animals can run extremely fast on land, and, in the water, can swim as fast as dolphin. Many fatalities occur when people are washing or gathering food near river banks. Kills: An estimated 600-800 people a year. Deadly technique: Crocodiles will grab their victims with terrifying speed, and often launch into a 'death roll', weakening its prey, dragging it under water and drowning the victim. Lives in: Africa and Australia
Out of the 1,500 species of scorpion, the African spitting scorpion is thought to be the most deadly, and can spray its venom up to a metre. Arounf 25 species of scorpion are thought to be deadly to humans. Kills: An estimated 800-2,000 people a year. Deadly technique: Scorpions use their tail stingers to paralyse their prey with venom. Lives in: Worldwide; particularly Africa, the Americas and Central Asia.
Weighing in at up to eight tons, although beautiful creatures, elephants can be lethal. African elephants in particular can be aggressive, especially older bulls and young males. These creatures, unsurprisingly, are more aggressive in areas where poaching is rife or when their habitat is threatened. Kills: An estimated 300-500 people a year. Deadly technique: Most human deaths are result of the elephant trampling on its victim. Lives in: Africa and India
African lions are the biggest of the big cats, and are known to kill around 70 people in Tanzania alone every year. With the destruction of their habitat, human attacks by leopards in India, and the North American mountain lion are thought to be on the increase. Kills: An estimated 800 people a year. Deadly technique: African lions will often use strangulation to kill their prey, while tigers will attack from the back and aim for the jugular, and mountain lions will maul their victims. Lives in: Africa, North America, and India