Labrune takes over as Marseille president
Margarita Louis-Dreyfus said in a statement on the club's website that the change had to be made because OM are facing new challenges, including the renovation of the stade Velodrome.
Dassier, 69, was named as Marseille president in 2009, leading the club to a League Cup and Ligue 1 double last year. OM also won the League Cup this season.
Labrune, 40, was late OM president Robert-Louis Dreyfus's communications director before he was appointed president of the club's supervisory board in 2008.
Coach Didier Deschamps agreed to extend his contract with the 2010 French champions this month despite tensions with Dassier over the club's policy.
Marseille will take part in the Champions League next season after finishing second in Ligue 1.