Passengers were evacuated via emergency slides after the Jet Airways Boeing 737, bound for Mumbai with 154 passengers and seven crew on board, ended up on the grass.
Passenger Rajeev Kumar said: “As the flight ran on the runway, it could not take off. Instead it skid off the runway and smoke started coming out.
“Chaos ensued and my foot was fractured.”
Another passenger, BK Singh, said several people had been injured while jumping onto the runway.
Parakh Hans, who was also on the flight, said: “There were pregnant women (on board), there were newborn babies.
“It is very sad what happened on the ground. But luckily it happened on the ground.”
The airport in western India is run by the country’s navy.
“There are minor injuries, bruises or fractures to 15 passengers,” said navy spokesman DK Sharma.
The airline said in a statement: “The flight 9W 2374 from Goa-Mumbai skidded off the runway at Dabolim airport this morning due to a technical glitch while aligning for take-off.
“All guests and crew members have been safely evacuated.
“However, a few guests have sustained injuries during the evacuation process (and) are being provided medical assistance.”
An investigation has begun.
Alternative arrangements would be made for the passengers, Jet Airways said.