In a videotape sent to Aljazeera, the captors identified themselves as the 1920 Revolution Brigades, a group which has previously seized foreigners working with US forces.
In the footage, which ran on Friday the man, who is of Lebanese origin, was shown holding papers identifying him as Dean Sadik.
The captive asked all foreign contractors who cooperate with the company he works for to stop dealing with it. Sadik worked for a company called Sky Link as the manager of the Baghdad airport building.
Unlike some previous videos of kidnappings in Iraq, no fighters appeared in the background.
Armed fighters, bent on evicting foreign forces from Iraq, have seized hundreds of Iraqis and foreigners in recent months. Some have been freed while at least 35 foreigners have been killed.