The fighter gave himself up when he was approached near the town of Sinjar on Monday morning, an Iraqi Kurdish general said.
He was reportedly carrying a large quantity of cash, three phones and a US driving licence.
The US is leading an international military coalition against IS.
The US state department said that it was aware of reports that a US citizen had been captured by Kurdish forces in northern Iraq, Reuters reports.
"We are in touch with Iraqi and Kurdish authorities to determine the veracity of these reports," a state department official said.
CBS News said the man was trying to enter Turkey when he was intercepted by Kurdish forces.
Maj Gen Feisal Helkani of the Kurdish peshmerga forces said the man was currently being held by the peshmerga for interrogation, AP reports.
US officials are checking reports that an American member of the so-called "Islamic State" group (IS) has been held in northern Iraq.