A US army spokeswoman inside the compound confirmed the explosions.
Immediately after the explosions around midnight (21:00 GMT) sirens could be heard coming from the direction of the US headquarters on the west bank of the Tigris river and helicopters buzzed over the area.
The compound is a sprawling complex of palaces and parkland which the US authorities in Baghdad have turned into a heavily defended fortress.
Earlier on Thursday, one US soldier was killed and 14 others wounded when at least one bomber blew up a truck at an American army base outside Ramadi.
US military officials said the bomb was concealed in a
furniture truck. The vehicle was driven by a bomber and
it is believed that two other Iraqis in the truck also died in the explosion.
At least 196 US troops have been killed in Iraq since US President George Bush declared an end to major combat on 1 May.
“A very, very loud explosion went off and shook my shop,” said Muhammad Hamad Majid, who runs his business 700m from the Ramadi camp where a residential zone begins.
“I went outside and saw a column of smoke rising in the sky from inside the base,” said the 35-year-old.
Delivery and construction trucks are allowed inside the compound, a few km from the town, on the east bank of the Euphrates river.
Meanwhile, two journalists from the US weekly newsmagazine Time and two American soldiers have been wounded by a grenade explosion while on a patrol in Baghdad.
A US military official said the attack took place late on Wednesday as the journalists accompanied troops. He declined to name the wounded.
At least 17 journalists have died in Iraq covering the war to topple Saddam Hussein and its aftermath, including at least four killed by US forces.