Kreuzer said Rodolfo Esteban Cardoso would take over on an interim basis for the second time, assisted by Hamburg youth team coach Otto Addo, a former player.
Fink's side was routed 6-2 by Borussia Dortmund on Saturday and humbled 5-1 at home by Hoffenheim earlier. The team has conceded 15 goals and secured only four points from five matches.
"We've made a bad start. We haven't impressed in games. We've no consistency, no clear structure," Kreuzer said. "It's well known we had this inconsistency last year. We wanted to get rid of it this year."
Fink, a former Bayern Munich midfielder who joined Hamburg from FC Basel in October 2011, was criticized for giving his players two days off after the loss to Hoffenheim, and his decision to fly home to his family in Munich after the loss to Dortmund also raised eyebrows.
"The decisions he made were somewhat unfortunate at the end of the day," Kreuzer said. "We didn't have the 100 percent confidence that he had the power to turn things around with the team."
Fink told a local radio station earlier Monday that he is "proud to have been here the two years. I trained a great club . it's still early enough now to achieve the (season's) aims, even with another coach."
The Hamburger Abendblatt newspaper reported that Hamburg is already in talks with former Hertha Berlin and Hoffenheim coach Markus Babbel as a successor, though Kreuzer dismissed the speculation, saying the names being mentioned in the media "make me smile."
Hamburg midfielder Rafael van der Vaart earlier voiced his disappointment with Fink's departure.
"Before the northern derby with Werder (Bremen). I don't really understand the timing," Van der Vaart said.
Kreuzer said, "I can understand that Rafael doesn't find this decision optimal. But we made it and Rafael has to accept it too."
