An American intelligence agency passed on the information, which pointed to Ansar al-Islam, a group based in northern Iraq that is suspected of recruiting holy warriors in Europe for suicide missions in Iraq, Hamburg's top security official, Dirk Nockemann, said.
Hamburg police said it had "concrete indications of people who want to carry out attacks by means of a car bomb" on the hospital, located in the Hamburg suburb of Wandsbek.
"Those potentially involved are believed to be from an Islamic terrorist background," the police said in a statement.
The northern German city of Hamburg was home to an al-Qaeda cell that included three of the Sept. 11, 2001 suicide pilots.
The police statement said state officials evaluated the threat as "very serious," immediately ordering enhanced security at the hospital.
At the nearby Wandsbek-Gartenstadt subway station, officers with submachine-guns and bulletproof vests checked the identity cards of residents trying to reach their homes.
The area around the clinic swarmed with police officers, who had dozens of vehicles at the scene.
Nockemann said "there are no indications so far that anything has been found at Wandsbek."
Nockemann said U.S. military installations in the Frankfurt area also had been threatened. However, spokespeople for Frankfurt police and for U.S. Air Force Europe said they had received no notification of a terrorist threat.