Lieutenant Colonel Muhammad Ahmad of Samarra police told reporters the soldier was taken captive on Monday night by fighters in two Opel cars.
He said US troops were out in force in the streets of the city on Tuesday.
A US military spokesman said he had no information on the incident.
Ahmad said the Americans had alerted Iraqi security forces and asked them to look out for the missing soldier.
US and Iraqi forces stormed Samarra, 100 km north of Baghdad, in early October as part of the US-backed interim government's campaign to retake areas under resistance control before national elections scheduled for January.