On Tuesday, the US military said that the soldier, a linguist assigned to a reconstruction team, was handcuffed and forced into a vehicle.
The soldier, whose name has not been been released, was reported missing on Monday. He was last seen early on Monday afternoon and went missing at about 7.30pm.
The statement said US and Iraqi forces were conducting searches to find him.
Employees at a local television station, Al-Furat TV, said that US soldiers told them the missing man, reportedly an American of Iraqi descent, had gone missing after leaving work to visit relatives in the city's Karrada district.
Residents in Karrada said that US forces sealed the central Baghdad district, conducting door-to-door searches and bringing in at least two tanks and two armoured vehicles.
Military officials in Washington told AP news agency that the soldier may have been abducted.
The last time any US soldiers were reported missing was in June, when two disappeared following an attack by fighters on a checkpoint south of Baghdad.
The two soldiers' bodies were later found bearing signs of torture. One of the soldiers had been beheaded.
Al-Qaeda in Iraq said it killed the soldiers, according to an internet statement.
Meanwhile, Mahdi Army fighters loyal to Muqtada al-Sadr, the radical Shia cleric, have killed four policemen affiliated with the Badr Brigades, a rival militia, in the southern city of Amara.
At least 25 policemen and Shia
fighters died last week in Amara
The attack came despite a public call by al-Sadr to halt the tribal vendetta, suggesting that splinter groups were developing within his militia.
Violence erupted in Amara after British forces handed over control of the city two months ago.
At least 25 police and Mahdi Army fighters were killed late last week when the militia stormed into the city seeking revenge for the killing of its commander in the region.
The Iraqi government on Monday imposed a curfew on the city in a bid to stem the violence.
The spread of revenge killings among Shias in their southern heartland has opened a new and ominous front as US forces struggle to control anti-US and sectarian bloodshed to the north - especially in Baghdad.