The 47-year-old Slomka, who took over at Hamburg in February, was informed of the decision on Monday, club officials told reporters.
Hamburg director Dietmar Beiersdorfer said under-23 coach Joe Zinnbauer would take temporary charge of the first team.
Slomka was tasked with lifting Hamburg away from relegation last season but they still needed a playoff to stay up and protect their perfect record of having played in the top division every season since its creation in 1963.
The northern German club have made a bad start this season, losing two of their three games and drawing the other to sit in last place on one point, despite spending big in the transfer market.
Newcomers Lewis Holtby, U.S. international Julian Green and winger Nicolai Mueller have so far failed to deliver with Hamburg having failed to score yet while Swiss international Valon Behrami and centre back Cleber have failed to plug a leaky defence.
Hamburg, who lost 2-0 to Slomka's former club Hanover 96 on Sunday, take on champions Bayern Munich next weekend.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly and Justin Palmer)
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