Since requiring penalties to see off third-tier Energie Cottbus in the first round of the DFB-Pokal last month, Hamburg's league campaign has failed to take off.
A goalless draw at newly-promoted Cologne was followed by a 3-0 home defeat to Paderborn, who were also plying their trade in the second tier last term.
A 2-0 loss at Hannover on Sunday appears to have been the final straw for the club's hierarchy, who kept faith with Slomka after Hamburg narrowly avoid relegation last season.
The 47-year-old had taken over from Bert van Marwijk after the Dutchman was himself dismissed in February following a string of poor results.
A host of Slomka's backroom staff members will also depart, with Under-23 coach Josef Zinnbauer set to take charge of the first team until a permanent successor is found.
Zinnbauer must now prepare the players for a daunting home clash with champions Bayern Munich on Saturday.
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