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, he said.
U.S. 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.
"It is a terrible event," she said.
The U.S. has drastically reduced its forces in Germany over the last decade, but still has some 50,000 troops stationed here. It operates several major facilities in the Frankfurt region, including the Ramstein Air Base often used as a logistical hub for operations in Afghanistan or Iraq.
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.
Still, a member of the U.S. House Homeland Security Committee, Rep. Patrick Meehan, said in Washington that it looked like a terrorist attack. The chairman of the subcommittee that focuses on terrorism and intelligence added he did not have all the facts about the shooting yet and was still being briefed.
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.
"We just heard the shots," he said.
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."
Kosovo remained part of Serbia amid the collapse of former Yugoslavia in the early 1990s, but a struggle for independence by ethnic Albanians there eventually led to the Kosovo war in 1998. The bloodshed was halted only in 1999 when NATO stepped in and bombed Serbia, followed by the deployment of peacekeepers.
Kosovo was initially run by a U.N. administration, but it unilaterally declared its independence from Serbia in 2008 and it is now recognized by many states, among them the U.S. and most EU nations.
The NATO-led Kosovo Force (KFOR) still has some 8,700 troops there provided by 32 nations, NATO says. The U.S. currently provides some 800 soldiers, the third-largest contingent behind Germany and Italy, according to KFOR's website.
The American forces in Germany have been targeted in attacks in the past, including a 1986 bombing at a disco in then-West Berlin that was known to be frequented by U.S. servicemen. Two soldiers and one civilian were killed, and 230 others injured in that attack, which a Berlin court in 2001 ruled was organized by the Libyan secret service and aided by the Libyan Embassy in then-communist East Berlin.
The leftist terrorist Red Army Faction was also responsible for a string of attacks on Americans in the 1970s and 1980s before the group was disbanded in 1998.
More recently, German police thwarted a plot in 2007 to attack U.S. facilities by members of the extremist Islamic Jihad Union. Four men had planning to attack American soldiers and citizens at facilities including the U.S. Air Force's Ramstein Air Base in Germany but were caught before they could carry out the plot.