Three-foot Simon, a continental giant rabbit aged 10 months, was said to have been travelling from Heathrow to O'Hare in Chicago after being bought by a celebrity owner in the United States.
Breeder Annette Edwards, from Worcestershire, told The Sun that Simon was expected to grow to be the world's biggest rabbit after his father Darius grew to 4ft 4in (1.32m).
She told the paper: "Something very strange has happened and I want to know what. I've sent rabbits all around the world and nothing like this has happened before.
"The client who bought Simon is very famous. He's upset."
The breed costs £5,000 a year to keep, the paper said.
A United spokeswoman said: "We were saddened to hear this news. The safety and wellbeing of all the animals that travel with us is of the utmost importance to United Airlines and our PetSafe team.
"We have been in contact with our customer and have offered assistance. We are reviewing this matter."
It comes less than three weeks after a video showing passenger David Dao being dragged off a United Express flight sparked widespread outrage.
Dr Dao, a 69-year-old from Kentucky, was seen with a bloodied face after being forcibly taken off the plane by Chicago airport officers who had been summoned by United employees when he would not give up his seat.
Speaking after the incident, on April 9, United chief executive Oscar Munoz said: "The truly horrific event that occurred on this flight has elicited many responses from all of us: outrage, anger, disappointment.
"I share all of those sentiments, and one above all: my deepest apologies for what happened.
"Like you, I continue to be disturbed by what happened on this flight and I deeply apologise to the customer forcibly removed and to all the customers aboard. No one should ever be mistreated this way."