Club bosses held a crisis meeting late into Saturday evening in the wake of a 4-2 defeat to Eintracht Braunschweig - the seventh defeat in a row.
That result left Hamburg in 17th position, just one point above bottom-placed Braunschweig.
"We saw ourselves forced, at this time, to take this decision although at the same time, we regret it," said Hamburg's director of sport Oliver Kreuzer.
"We would like to thank Bert van Marwijk for his work."
Slomka, who was relieved of his duties as coach of Hannover just after Christmas, is expected to be installed as Van Marwijk's replacement with former Hamburg coach Martin Jol also tipped for a return.
Fulham coach Felix Magath had left himself open to a return until joining the Cottagers on Friday, claiming half of the northern Germany club's bosses were against his return.
Whoever takes over inherits a team in the worst situation in the club's history.
Hamburg are the only club never to have been relegated from the Bundesliga while their current losing streak is a new club record.
They have conceded 18 goals in five games since the turn of the year with Saturday's two against Braunschweig the first they had scored since before Christmas.
Their last win was against Hannover at the end of November.