Kreuzer arrived from Karlsruher in June 2013, but was present for one of the club's most challenging seasons in living memory, with Hamburg only avoiding relegation from the Bundesliga by virtue of an away-goals play-off victory over Greuther Furth.
The 48-year-old was thought to have a contract until 2016, but Hamburg confirmed in a statement on Monday that he had left the club "with immediate effect".
"We have certain plans in place during the sporting restructuring of the club," said new board chairman Dietmar Beiersdorfer. "This decision is one of them.
"I personally told Oliver Kreuzer the news this morning. Apart from that, the club would like to thank him for hard work during his time here.
"We would also like to express our appreciation for the way he helped and supported me during the transition to the Football AG [company structure] and with squad planning."
Beiersdorfer was presented as Hamburg's new chairman on Wednesday.
