The photo of the frat members holding a folded American flag at their waists was attached to an email about an upcoming party sent to a sorority, the Detroit Free Press said.
But various websites, such as Buzzfeed.com, got hold of the photo as well, the Free Press said.
The headquarters of Pi Kappa Alpha announced the suspension Tuesday and university officials said they are investigating.
Ryan Lee, 19, president of the suspended Beta Tau chapter, said the image and email were supposed to be funny and apologized if anyone took offense.
Justin A. Buck, executive vice president of Pi Kappa Alpha, said the chapter was being suspended "due to members displaying inappropriate and offensive photos."
It is not clear when the photo was made public, the Free Press said, but university officials found about it on Monday.