Ten passengers were treated at the scene, with six being taken to a hospital with minor injuries, said Thomas Bosco, Acting Director of Aviation for the Port Authority of New York and New Jersey, which oversees the area airports. The six crew members were taken to another hospital for observation.
Dallas-based Southwest said there were 150 people on Flight 345 coming from Nashville, Tenn., while the Port Authority said the total was 149.
Bosco said the nose gear of the plane collapsed when it landed at 5:40 p.m., and "the aircraft skidded down the runway on its nose and then veered off and came to rest in the grass area."
Bosco said there was no advance warning of any possible problem before the landing.
Emergency crews were seen spraying foam toward the front end of the plane on the tarmac. The Port Authority said the passengers exited the plane by using chutes.
The airport was temporarily closed, but one of two runways was operating shortly after 7 p.m., and Bosco said the Port Authority was hoping to have the airport fully open by Tuesday morning.
The FAA is investigating, as is the National Transportation Safety Board.
Richard Strauss, who was on a nearby plane waiting to take off for Washington, said the nose of the plane was "completely down on the ground. It's something that I've never seen before. It's bizarre."
A rear stairwell or slide could be seen extending from the Southwest flight, said Strauss, who owns a Washington public relations firm. His plane, which was about 100 yards from the Southwest flight, wasn't allowed to taxi back to the gate, he said.
Bobby Abtahi, an attorney trying to catch a flight to Dallas, was watching from the terminal and heard a crowd reacting to the accident.
"I heard some people gasp and scream. I looked over and saw sparks flying at the front of the plane," he said.
The incident came 16 days after Asiana Flight 214 crash-landed at San Francisco's international airport on July 6, killing two Chinese teenagers; a third was killed when a fire truck ran over her while responding to the crash, authorities said. Dozens of people were injured in that landing, which involved a Boeing 777 flying from South Korea.
Longtime pilot Patrick Smith, author of "Cockpit Confidential: Everything You Need to Know About Air Travel. Questions, Answers, and Reflections" and AskthePilot.com, said landing gear incidents are not high on the list of worries for pilots.
"It doesn't happen very often but I need to emphasize just how comparatively minor this is and how far, far down the hierarchy it is," he said. From a pilot's perspective, this is nearly a non-issue. They make for good television, but this is far down the list of nightmares for pilots."
Associated Press writers Amanda Barrett, Deepti Hajela and Jennifer Peltz contributed to this report.