Predecessor Bert van Marwijk paid the price for eight consecutive defeats in all competitions when he was sacked following last Saturday's 4-2 league loss to bottom-placed Eintracht Braunschweig.
That run has left Hamburg 17th in the table, just one point above Braunschweig and three from safety.
Former Hannover boss Slomka is Hamburg's eighth permanent manager in the last seven years as the seven-time German champions bid to avoid what would be a maiden relegation from the top flight.
Dortmund have returned from the winter break with a renewed vigour, scoring 13 goals in four league outings, from which they have gained 10 points.
That is the kind of form Jurgen Klopp's men were in when Hamburg were thrashed 6-2 at Signal Iduna Park in September, an ominous warning for the hosts.
Stuttgart are another team in freefall, but coach Thomas Schneider received a vote of confidence on Tuesday ahead of the home match against Hertha Berlin.
Schneider's 15th-placed side have lost six Bundesliga games in a row, leaving them looking nervously over their shoulders, but Hertha have fared little better in 2014, claiming just three points from 12 available since returning from the mid-season break.
Elsewhere on Saturday, an out-of-form Borussia Monchengladbach entertain Hoffenheim, struggling Nuremberg entertain rock-bottom Braunschweig, 16th-placed Freiburg host mid-table Augsburg, and Wolfsburg go in search of a third straight win when high-flying Bayer Leverkusen pay a visit.
Unbeaten leaders Bayern Munich are in action on Sunday, with Hannover aiming to become the first side to beat the defending champions in the league since October 2012.
Sunday's other game sees Werder Bremen travel to Eintracht Frankfurt, with the two bottom-half sides separated only by goal difference, while Friday's only match involves UEFA Champions League hopefuls Schalke and seventh-placed Mainz.
