"The board feel that, 17 games into the season, results have not corresponded with our objectives and a strong decision needed to be taken to get the team moving in the right direction again in the coming weeks," reads a statement on the club's official website.
Club president Vincent Labrune said that the decision to dismiss Baup is "the most difficult and painful I have had to take since I came to the club".
"Elie Baup is unanimously appreciated for his qualities as a person," he added. "Nobody can forget the job he has done at Olympique de Marseille. He allowed us to finish second last season when nobody expected us to.
"But this season he has not obtained the expected results. The team has not shown the desire or the quality that we have the right to expect, especially at a club like Olympique de Marseille.
"As is unfortunately the case in these circumstances, the coach pays the price for poor performances, but I now expect a quick reaction from the players."
Marseille sporting director Jose Anigo will be in charge of the first team until the winter break.