The interior ministry said that the men used three vehicles and kidnapped 26 workers, including three women, at a food plant in southwest Baghdad on Sunday.
The men were all wearing civilian clothes and rounded up every worker in the factory, known for making kibbeh, a kind of meatball, in Baghdad's lower income Amil neighbourhood.
The identity of the kidnappers was not known. Similar mass kidnappings happen frequently in Baghdad for both political and criminal motivations.
The breakdown in security in the violence-prone streets of Baghdad has resulted in a rampant kidnapping industry with ransoms in the neighbourhood of tens of thousands of dollars.