The crew of Alitalia Flight 608 approaching John F. Kennedy airport on Monday reported the sighting.
"We saw a drone, a drone aircraft," the pilot can be heard telling air traffic controllers on radio calls captured by the website LiveATC.net.
The FAA said it was investigating the incident.
The Alitalia aircraft did not take any evasive action and landed safely.
The FBI expanded on the FAA report, saying in a statement that the Alitalia flight from Rome was roughly three miles from runway 31R when the incident occurred at an altitude of approximately 1,750 feet.
The unmanned aircraft, described by the FBI as black and no more than three feet wide with four propellers, came within 200 feet of the Boeing jetliner.
The FBI said it was looking to identify and locate the aircraft and its operator. A source with knowledge of the incident says investigators interviewed the pilot and others on the Alitalia plane.
"The FBI is asking anyone with information about the unmanned aircraft or the operator to contact us," said Special Agent in Charge John Giacalone. "Our paramount concern is the safety of aircraft passengers and crew."
Air traffic controllers warned other planes approaching the JFK runway of the drone report, but at least two other pilots radioed they did not see it.
A spokesman for the New York Police Department was not aware of the incident and the Port Authority of New York and New Jersey, which operates the airport, referred CNN to the FAA.
Unmanned aerial systems, sometimes called drones, and other remote-controlled planes could pose a risk to larger passenger aircraft if they collided or were sucked into an engine.
For recreational hobbyists, flying remote-controlled planes is only allowed by the FAA up to 400 feet, and within sight of the operator. If they are going to fly within three miles of an airport, they have to let air traffic controllers know.
Flying unmanned aerial vehicles is illegal for most business purposes; however, governments and public entities such as police departments can apply for permission to operate them.
The FAA has been working to setup new rules and to safely integrate the use of unmanned aircraft into the national air space, and last year opened an "unmanned aircraft systems integration" office.
CNN's Carol Cratty and Rob Frehse contributed to this report.