He was arrested late on Thursday, along with three other suspects, during operations in the Mashru area in the province of Wasit, south of Baghdad.
The most prominent Shia militia, the Mehdi Army, has been observing a ceasefire since August.
The US military has accused what it calls rogue elements of failing to observe the truce.
The ceasefire is due to expire at the end of February, and correspondents say it is not clear if it will be renewed.
A US military press release said the arrested man was believed to be a "special groups" leader - language the military uses to describe Shia militias allegedly backed by Iran.
Correspondents say the US military has been careful not to accuse Moqtatda Sadr, the leader of the Mehdi Army, himself of any role in attacks by Shia militants.
They instead blame rogue militiamen violating his cease-fire order.