Pilots turned the Madrid-bound Iberia Air Lines plane Sunday around "due to a fire warning light for the No. 2 engine," said Arlene Salac, a spokeswoman for the Federal Aviation Administration.
All passengers and crew were evacuated after the Boeing 747 landed at about 7:20 p.m., Salac said.
Firefighters extinguished the blaze, which was contained to the engine, she said. The cause was under investigation.
"We turned around in the air because the plane was on fire, I think the engine," said passenger Carol Dunning.
Passenger Georg Hutter of Vienna, Austria, said he was seated at the back of the jetliner, on the left side, and saw smoke and flames through the window.
"While he was taking off, it was all smoke. We saw it from the passenger compartment," Hutter said. "The engine was taking more fire; the flames were coming more and more."
Hutter, who is a private pilot, said the passengers remained calm as the pilots informed them that the jet was turning around.
Another passenger, Chris Miros of Bayonne, N.J., said "people started freaking" when the plane landed and they had trouble opening two emergency doors.
His elbows were bandaged after he scraped them while jumping down the emergency evacuation slide.
Seven people were taken to Jamaica Hospital with injuries sustained in the evacuation, hospital spokesman Michael Hinck said. A 56-year-old man who suffered head injuries was in critical condition Monday, and a 60-year-old woman was in stable condition. The other five were treated and released, he said.
An employee in Iberia's press office, Consuelo Arias, said the plane had passed an overhaul inspection last February and had logged only 2,000 flight hours. She did not know how long the plane had been in the air when the alarm sounded, but said it had reached an altitude of only 1,000 feet.
"We heard that everything was perfectly OK and we heard that the crew had everything under control," Arias. "It seems like the crew did well."
Arias said she had no information on the passenger's claim that there had been difficulty opening hatch doors during the evacuation.