Australian-owned security firm based in Dubai says it “deeply regrets” incident.
Most troops stationed at Camp Victory are American but other coalition soldiers are based at the complex near Baghdad International Airport.
No further details on the attack were immediately released.
Camp Victory and other US bases in Iraq have frequently come under fire, but attacks with such a large number of casualties are rare.
The US military meanwhile said 13 armed fighters, including three members of al-Qaeda in Iraq responsibile for the assassination of a Sunni Arab preacher, have been killed in an air strike.
The strike on Wednesday west of Baghdad came hours after the imam, identified as Abu Bilal, was killed.
“Three of the al-Qaeda in Iraq members killed in a coalition air strike Wednesday following their assassination of a local imam have been identified as Abu Rami, Ammar Fadhil Kadhim and Fadil Salman,” the military said.