The Dynamic Airways Boeing 767 was on the runway at Fort Lauderdale-Hollywood International Airport, preparing for departure to Venezuela.
The left engine, which had been leaking fuel, caught fire.
The passengers and crew were evacuated and the fire extinguished but one person has been left with severe burns.
"The crew followed the emergency procedures, shut down the engine and evacuated the aircraft in order to assure safety to all on board," Dynamic Airways said in a statement.
Those hurt are being treated at Florida Broward Health Medical Center in Fort Lauderdale.
One person has been "seriously burnt", according to Mike Jachles of the Broward County Sheriff's Office.
The National Transportation Safety Board is sending agents to Fort Lauderdale to investigate the fire.
Dynamic flies between Fort Lauderdale, New York, Venezuela and Guyana.
Fifteen people were injured when a plane's engine caught fire as it taxied for take-off from an airport in Florida.