The club described the Peruvian striker's behaviour as "absolutely unacceptable" and said he would face a heavy fine.
"I had a blackout," Guerrero told the club's website after the latest incident in an unhappy season in which he has also suffered a knee injury and battled against a fear of flying.
"I was insulted and I overreacted. I'm really sorry for it.
"I hope I have the chance to meet the fan in person to apologise. I've already apologised to HSV. Naturally, I will accept any fine from the club."
Chairman Bernd Hoffmann said: "Paolo's behaviour was absolutely unacceptable. That sort of thing should not happen.
"Paolo will be punished by us with a big fine."
It was only Guerrero's second league match since he tore cruciate knee ligaments in September.
"Paolo made a big mistake in the heat of the moment. But there is no rift between the team and the fans. We must stay together to reach our goals," he said.
