Flight EZY6056 departed from the Spanish city on Saturday with the group still in the airport due to "an issue at the boarding gate".
Hold luggage had already been loaded on to the aircraft for the 9.15pm flight from Malaga, leaving passengers with only their hand luggage.
A spokeswoman for the airline said 19 customers took the next available flight to Gatwick at 10.30pm.
The remaining 10 spent the night in Malaga before flying to Bristol the next day.
"EasyJet is in the process of contacting and apologising to the 29 passengers who did not board their flight from Malaga to Bristol on Saturday 5 October due to an issue at the boarding gate," the spokeswoman said.
"We have launched an investigation to understand what happened and will be offering flight vouchers and a refund of onward travel arrangements from Gatwick as a gesture of goodwill to the affected passengers.
"EasyJet arranged for 19 passengers to travel on the next available service to Gatwick and arranged accommodation for 10 passengers who travelled to Bristol the next day."
A total of 110 passengers were able to board the plane but it is believed a second barrier then did not open for the remaining 29.
The group queued in the corridor behind the second barrier - where they watched as their plane took off.
Iain Locke, 58, of Pensford in Somerset, told the Bristol Post the group were trapped in the corridor for 20 minutes.
Mr Locke told the paper: "I turned round to the guy beside me and said 'I don't want to alarm you, but the plane has gone'. I just couldn't believe it.
"I've flown a lot and I know there are measures in place for the pilot and crew to check the correct number of passengers are on the aircraft.
"I find it unbelievable that a flight could take off with passengers missing."
The luggage was flown to Bristol Airport, where it was reunited with the passengers after their flights home, the easyJet spokeswoman said.