A military spokesman for the First Armoured Division said the ambush took place in the al-Karrada district at around 22:30 (19:30 GMT) on Wednesday.
A second soldier and an interpreter were also wounded after resistance fighters targeted the Taskforce 1 convoy, bringing the number of US wounded to 2200.
With US-led occupation forces under constant threat, a partner in Japan's coalition government may face problems in finalising plans to send troops to Iraq.
Risks affect deployment
Takenori Kanzaki, whose Buddhist-backed New Komeito party has expressed reservations about the troop dispatch, is in Kuwait and will decide soon whether he can travel to southern Iraq to check on security there, a party spokesman said on Thursday.
Japan last week approved a plan to dispatch up to 600 ground troops to southern Iraq for reconstruction and humanitarian work, a decision critics say could violate the nation's pacifist constitution by sending the military to an overseas war zone.
Kanzaki has signed off on the troop dispatch. But many members of his party - one of whose core tenets is pacifism - remain opposed.
"If he can go to southern Iraq, return and say it's safe, he can counter that opposition. If he can't go because it's too dangerous, the damage to Koizumi would be big"
professor at Chiba University
Political analysts said his planned trip to Iraq was probably designed to demonstrate that the southern sector was safe and that troops would not risk being dragged into combat.
"If he can go to southern Iraq, return and say it's safe, he can counter that opposition. If he can't go because it's too dangerous, the damage to Koizumi would be big," Chiba University professor Muneyuki Shindo added.
"And if something happened to him there, the dispatch would be off. It's a big risk."
Defence Minister Shigeru Ishiba was expected to firm up some of the dispatch plans after a meeting with Koizumi, possibly later on Thursday.
He might announce that a small advance air force contingent would leave for Kuwait and Qatar on 25 December.
Japanese media have said that the first substantial army contingent would head for Iraq in February.
Koizumi must balance the demands of Japan's alliance with the United States, keen to see Japanese "boots on the ground", with voters' concern that the military will be the target of attacks.
Those worries mounted after the death of two Japanese diplomats last month and persist despite the capture of fallen Iraqi leader Saddam Hussein.