The incident happened at a downtown Atlanta club on March 16 during a mix-tape release party, CNN reported Sunday.
The victim told police that he tried to start a conversation with the 33-year-old rapper, whose real name is Radric Davis.
"I'm in the military. I wanted to get a picture with Gucci Mane," the man told CNN affiliate WSB-TV. "I was speaking to the security guard, and Gucci Mane hit me in the head with a bottle."
The man, whose name was not reported, suffered a deep gash on his head, Atlanta Police Sgt. Greg Lyon said.
Davis is now wanted on aggravated assault charges.