Fire department spokesman Kevin MacGregor said a building engineer suggested the fire might have started in the ventilation system. He didn't know of any injuries.
At least a dozen ambulances and fire trucks were at the scene, just south of Chicago's downtown business loop.
MacGregor said it was unclear if the fire was related to the filming.
Firefighters said the blaze was discovered on the roof of the Near West Side facility, which spans the Eisenhower Expressway near Canal Street.
The new Batman movie "The Dark Knight" is being filmed near the scene. A safety officer for the movie tells WBBM-TV, a fan on the roof may have contributed to the fire by igniting some garbage after shorting out. But the Fire Department said it was not clear if the fire was related to the filming of the movie.
Pete Kearney, who works in an office building next to the old post office, said he noticed smoke outside his 11th-floor window and went outside to check it out.
He said crews had been filming there all week, so "we assumed it was part of the movie."
Letters affixed to the side of the old post office read: "Gotham National Bank."