Kosovo's interior minister told The Associated Press that German police have identified the shooter as a man from Kosovo. The attack came as the bus sat outside Terminal 2 at the airport, according to Frankfurt police spokesman Manfred Fuellhardt.
The bus driver and a passenger were killed, and one person suffered serious wounds and another light injuries, Fuellhardt said.
He had no further details, but US Air Force Europe spokeswoman Maj Beverly Mock said all four victims were airmen. She said she could not yet say where they were based, nor give any other details until their next of kin had been notified.
In Berlin, German Chancellor Angela Merkel said her sympathies were with the victims and their families, and pledged that Germany would do everything in its power to investigate the crime.
At the airport, taxi cab driver Salimi Seraidon said he was sitting at a stand about 200 yards (meters) away when the attack took place and said it was over quickly as police rushed onto the scene.
Kosovo Interior Minister Bajram Rexhepi told AP that German police have identified the suspect as Arif Uka, a Kosovo citizen from the northern town of Mitrovica.
"This is a devastating and a tragic event," Rexhepi said. "We are trying to find out was this something that was organized or what was the nature of the attack."
The German news agency DAPD quoted Hesse's state interior minister, who had rushed to the scene of the shooting, as saying there were no indications of a terrorist attack.