The spokesman said Qasim Muhammad al-Ubadi, assistant director of the hospital, died in a "terrorist act" late on Monday but did not give details of how he was killed.
Fighters who oppose the US installed interim Iraqi government have killed several senior officials in recent months by shooting or bombs, accusing them of collaborating with US occupation forces.
On Monday a senior Interior Ministry official was gunned down near his home in Baghdad.
Aljazeera's correspondent in Baquba qouted a US military source as saying one US soldier was killed in the eastern Iraqi city.
Iraqi fighters had destoyed an Iraqi truck carrying cement barricades for the US army.
A US patrol arrived at the scene to find itself face to face with a human bomber driving a car towards it and blowing himself up on impact with the US military hardware killing one soldier and wounding others, according to the US army.
Series of attacks
Mortar shells rained on the green zone where the US-led occupation authorities are stationed.
The mortar round was one of several loud blasts that echoed across Baghdad early on Tuesday.
File picture: Smoke billows from
the US occupied green zone
A US army spokesman said fourteen US soldiers were wounded and several cars were destroyed in the attack. An Iraqi refuse collector was also killed in the attack.
Mortars have often been fired at the Green Zone compound, which was the Iraqi Republican Palace before the fall of Baghdad in April 2003.
Baghdad has experienced almost day-to-day attacks since 28 June when the US transferred power to an Iraqi interim authority.
In the town of Falluja, west of the capital, six Iraqi civilians, including two women and a little girl, were wounded by gunfire, that residents blamed on US forces, police said.
The US military was unable to confirm the incident.
In Balad north of Baghdad, a US contractor was wounded in a shelling on a US military base in the town.