According to television pictures Guerrero – who recently returned from a seven-month injury absence – was leaving the pitch when the fan targeted the player with insults, telling him to go back to his country.
Guerrero reacted by throwing a bottle at the supporter, striking him on the head. He was then ushered into the dressing room by one of his team mates.
It was not clear whether the bottle was plastic, or made of glass.
Hamburg president Bernd Hoffmann said Guerrero was now facing certain sanctions.
"No matter what the supporter said, this is something that simply should not happen. It's unacceptable, and we will make sure he is punished," said Hoffmann.
The German league's disciplinary federation could also become involved in the affair.
After a promising start this season Hamburg are currently sixth in the Bundesliga, 16 points behind leaders Bayern Munich.