Saturday's heavy defeat leaves Hertha two points from the relegation places in the league table, which the club's CEO Carsten Schmidt described as "a very precarious situation".
"After much deliberation, we feel that a change of head coach can give the team fresh impetus," Schmidt added in a statement.
Labbadia, 54, took charge in April 2020 and kept Hertha in Germany's top flight last season, but the team has taken just one point from four games in 2021.
He is replaced by caretaker coach Pal Dardai, who was in charge of the first team from 2015 until 2019 before being moved to the club's youth academy.
Schmidt said Hertha expects to name a permanent head coach "in the coming days".
Preetz, 53, was shown the door after 25 years with Hertha, first as a player, then eventually becoming general manager in 2009.
He has been axed for failing to move Hertha forward despite the spending of around 100 million euros ($122 million) in transfers last season, funded by the club's wealthy backer Lars Windhorst.
Sports director and former Germany defender Arne Friedrich will take over Preetz's responsibilities until the end of the season.
Hertha face a tough run of fixtures next month with Bundesliga leaders Bayern Munich and RB Leipzig, who are currently second, both visiting Berlin's Olympic Stadium in February.