The spokesman said the building was hit between 0500 and 0530 (1300-1330 GMT) on Thursday. US ambassador John Negroponte was not in Iraq at the time of the attack.
“One of the injured was shaken. The other injured person required medical treatment but the injuries are not severe,” the spokesman said, adding the roof was slightly damaged in the attack.
The US embassy in Baghdad, the largest US mission in the world, is in the heavily fortified Green Zone, which also houses the offices of the US-appointed Iraqi interim government.
Iraqi resistance fighters have routinely launched mortar and missile attacks against the Green Zone, which used to house the main palace of former leader Saddam Hussein.
Meanwhile, the Polish news agency PAP quoted a military spokesperson who said two Polish soldiers were killed and five injured in a road accident in Hilla after their patrol was fired on near their Babylon base on Thursday.
The US Department of Defence reported that one US soldier was killed on Wednesday.
The latest toll brings to 953 the number of US fatalities in Iraq since the 20 March 2003 invasion of the country.
Sixty-five military personnel from other countries have also been killed since that date.