The amount of the fine was not publicised by the club but it is believed to be between €50,000 and €100,000, which will go towards charitable projects.
"What prompted us to take this decision was the fact that Paolo made a sincere apology and that in four years at Hamburg he has never committed a comparable act," explained Hamburg president Bernd Hoffmann.
"His behaviour is in no way acceptable but we think he deserves a second chance."
The incident took place following Hamburg's goalless league draw at home to Hannover on Sunday.
Guerrero was making his way towards the tunnel at the HSH Nordbank Arena when he was insulted by a fan in the stands, who reportedly told him to go back to his own country.
According to images broadcast by Sky Germany television channel, Guerrero responded by throwing a drinks bottle that he was carrying at the supporter, striking him in the head.
The Peruvian, who recently returned to action after seven months on the sidelines with a serious knee injury, was then persuaded to return to the changing rooms by one of his team-mates.
The supporter, who was not hurt in the incident, did not press charges.
Guerrero will apologise in person prior to the home leg of Hamburg's Europa League quarter-final tie with Standard Liege on Thursday, the club said.
"What I did was not good at all. It was a huge mistake and I am really sorry about it," said the player in a statement released by his club.
Guerrero, whose contract with Hamburg expires at the end of the season, could still be made to appear before the disciplinary committee of the German Football Federation, who have the power to suspend him.