The 25-year-old was out with team-mate Julian Schieber when he was spotted by a 34-year-old man, who promptly shouted out his name.
The Germany international responded by throwing a doner kebab at the man, who went to the police, claiming that his eyes were burning after being hit in the face by it.
"It is true that a complaint was filed against Mr Grosskreutz. We have started a criminal case for willful injury," a police spokesman has confirmed.
Schieber, meanwhile, has leapt to the defence of his friend and team-mate, claiming he came in for hostile treatment from Koln fans.
"There was a group of young fans who sang songs about Kevin. He felt that they were mocking him and threw his kebab."
Grosskreutz has apologised for his actions, admitting they were ill thought out.
"I perceived the situation as insulting and it offended my privacy," he said.
"Of course, it would have been better if I hadn't thrown the doner in public. There is no doubt that this situation isn't ideal. I'm sorry."