Bremer admitted the attack took place on 6 December when questioned by reporters in the southern Iraqi city of Basra.
"That's correct," Bremer said on Friday, before laughing off the incident.
No further official details are available, but a US television network has reported that Bremer escaped unharmed when his convoy hit an explosive device and came under fire as it drove from Baghdad airport.
The convoy was able to speed away and no one was injured.
The incident, which occurred on the same day US Defense Secretary Donald Rumsfeld arrived in Baghdad, was not reported to the press by Bremer's Coalition Provisional Authority (CPA).
Occupation forces have met with constant resistance in many parts of the country, but especially in areas in and around Baghdad.
The assassination attempt highlights the considerable dangers occupation forces run when travelling on Iraq's roads.
Bremer, 61, heads the US-led occupation forces which have been ruling the country following the overthrow of Saddam Hussein last April.
The former foreign service officer is charged with overseeing political and reconstruction efforts in Iraq.
He served for 23 years in the State Department and held a variety of senior posts, including top aide for six secretaries of state.
His foreign service career has included stints in Malawi, Norway, the Netherlands and Afghanistan.