Two F-16 jets were launched at the request of the pilot "out of an abundance of caution," according to one official cited by NBC New York.
A law enforcement official said the incident wasn't thought to be terrorism.
The North American Aerospace Defense Command (NORAD) scrambled two F-16 jets to shadow Flight 34 until it landed safely at New York's John F. Kenney International Airport shortly after 4 p.m., the Transportation Security Administration said in a statement.
"At approximately 3 p.m. ET, the Transportation Security Administration (TSA) was notified of passengers allegedly behaving suspiciously onboard American Airlines Flight 34 from Los Angeles International Airport (LAX) to John F. Kennedy International Airport (JFK). Out of an abundance of caution, NORAD scrambled two F-16 jets to shadow the flight until it landed safely at JFK at approximately 4:10 p.m. ET. Law enforcement met the flight and will interview passengers," according to a statement by the TSA.
A NORAD spokesman said the three passengers locked themselves in the bathroom and were still inside when the plane landed. The FBI was responding to the airport. The official was not authorized to speak publicly and spoke to The Associated Press on condition of anonymity.
A NORAD spokesman confirmed the military aircraft intercepted the flight about 100 miles west of New York and shadowed it until it landed.
American Airlines is owned by parent AMR.
TV Crew Truck Causes Scare at Dallas Airport
Separately, an FBI official said a rented moving truck parked at a curb at the Dallas-Fort Worth airport caused a brief scare on the 10th anniversary of the Sept. 11 terrorist attacks.
FBI official Kevin Gentry said the truck was driven by a crew member of the Discovery Channel show "Sons of Guns." Investigators were suspicious because the driver said, "I got a couple of guns," but Gentry said he was just waiting for a co-worker. The two will film in El Paso and Albuquerque, N.M.
Airport spokesman David Magana said a bomb squad and canine units were deployed when an automatic weapon was found in the truck, parked in an area where troops returning from Middle East stints are greeted.
A Discovery Channel spokesman was not immediately available to comment.
Three Detained at Detroit Metro Airport
Elsewhere, three passengers were being questioned and more than 100 were detained at Metro Detroit Airport, according to The Detroit News.
Officials at the airline told the Detroit News that the flight, which originated in San Diego, was directed away from the concourse after two passengers were "observed behaving suspiciously … spending an extraordinarily long time in the lavatory."
"The airport can confirm that there was only ONE plane being investigated by police. The pilot initially speculated that three people were behind the suspicious incident," according to Scott Wintner, Wayne County Airport Authority for Detroit Metro Airport. "Reports of three specific people being held in custody are not confirmed, instead the airport confirms that police have been interrogating ALL passengers and crew aboard."