The kidnapping occurred, the official said, after the Americans were invited into the home of their interpreter in the southern Baghdad neighbourhood of Dora.
There were no immediate claims of responsibility.
Kidnappings in Iraq have been carried out by the Islamic State group, Shia militias and criminal gangs often demanding ransom payments or seeking to resolve workplace disputes.
In mid-December, gunmen kidnapped at least 26 Qataris from their desert hunting camp in Iraq near the Saudi border.
The US citizens were kidnapped days after leaders of the Popular Mobilisation militia issued threats against US forces in Iraq for their "colonial ambitions" in the country, as they said.
