The Bundesliga outfit have parted ways with the 45-year-old five games into the season after a wretched start to the new season
The club have just one win and three losses in five games to start the season and have the worst defensive record in the league to date, having conceded 15 goals.
In his two seasons with the club, Fink could not return the team to past glory, leading them to seventh and 15th-place finishes, failing to finish in the European places and narrowly avoiding relegation.
Hamburg were dominated by Borussia Dortmund over the weekend, suffering a 6-2 defeat at the Signal Iduna Park, sealing the fate of the former Basel coach.
"I am proud to have been at this club for two years. I've coached a great club," Fink told NDR.
"There's still plenty of time for HSV to achieve the goals they set at the start of the season."
The club have yet to name a replacement as they prepare to host arch rivals Werder Bremen on Saturday.