Everyone has been evacuated from the plane.
10 people suffered minor injuries and have reported "back and neck pain". Six people were taken to Elmhurst Hospital while four others refused treatment.
It happened on Southwest Flight 345 from Nashville around 6 p.m. on Runway 4.
The flight took off at 2:33 p.m. local time from Nashville. It was scheduled to arrive at LaGuardia at 5:10 p.m.
There were a total of 143 passengers, a lap infant, and six crew members on board.
The FAA says LaGuardia Airport is not closed, but they are not accepting arriving flights.
Port Authority spokesperson Lisa MacSpadden tells ABC News that one of the airport's two runways will be open, but the other will remain closed indefinitely. She says, "Passengers need to be prepared for major delays."
She added that "a wheel popped off the aircraft's landing gear after landing."
Also, there was no fuel leak or fire but foam was deployed as a precaution.
Southwest released a statement saying, "Southwest Airlines flight 345 landed at New York's LaGuardia at 5:40 PM Eastern Monday evening from Nashville. The aircraft is a Boeing 737-700. Eyewitness reports indicate the aircraft's nosegear collapsed upon landing. There were 150 people on board including Customers and Crew. All Customers have been deplaned and transferred to the terminal. Initial reports indicate local responders are caring for five Customers and three flight attendants who have reported injuries at this time. Southwest is cooperating with local authorities, and the NTSB has been notified."
The NTSB is sending an investigator to the accident.
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.
Governor Andrew Cuomo released a statement saying, "Earlier this evening, the Port Authority Police Department and LaGuardia Airport staff took quick and decisive action to ensure the safety and well-being of the passengers of Southwest Airlines Flight 345," Governor Cuomo said. "We are all grateful that there were no fatalities and do not appear to be any serious injuries resulting from the collapse of this flight's landing gear. I commend the actions of the Port Authority personnel and all emergency workers who assisted with the safe evacuation of Flight 345's passengers and crew."
(The Associated Press contributed to this report)