The kidnappings happened early this morning as gunmen stormed houses in the Shiite neighborhood of Sadr City, kidnapping the men, two police officials said.
The officials said they suspect the kidnapped men were involved in prostitution and criminal activities. Some Shiite militias have been involved in attacks against suspected prostitutes and stores that sell liquor as a part of their campaign to impose Islamic laws.
All officials spoke on condition of anonymity because they were not authorized to speak to journalists.
Iraq sees near-daily bombings and other attacks often claimed by the Islamic State group, which seized about a third of the country last year.