"Syracuse, American 550, medical emergency, captain is incapacitated, request handling for runway," a transcript of the co-pilot's radio transmission said.
There were 147 passengers and a crew of five on board American flight 550.
"We are incredibly saddened by this event, and we are focused on caring for our pilot's family and colleagues," the airline statement said.
Another crew was sent to Syracuse to fly the plane to Boston.
The name of the pilot, 57, has not been released.
Passenger Louise Anderson, who was heading from Reno, Nevada, to Boston via Phoenix, said she had dozed off on the flight.
"What I woke up to was the flight attendant telling us we were making an emergency landing because the pilot was ill," she said.
She said rumors were circulating of the pilot's death in the Syracuse airport, but they were only confirmed by an announcement on their makeup flight to Boston.
Anderson said the mood on board then was somber, but she commended the crew's handling of a tragic situation.
Airline pilots must pass a physical exam every 12 months -- every six months for captains if they are 40 or older.
Steve Wallace, who led the FAA's accident-investigations office from 2000 to 2008, said it is rare for a pilot to become incapacitated.
"What is important is the consistent result - the plane lands safely," Wallace said. "The co-pilot is fully qualified to fly the airplane. It's rare, but they train for it."
Modern airliners are capable of largely flying themselves. There is a debate in aviation circles about whether over-reliance on automation is eroding the manual flying skills of pilots.
Even if planes can fly by themselves, however, incidents like Monday's help ensure that regulators won't allow unmanned cockpits - or even an unaccompanied pilot - anytime soon.