Andre Villas-Boas’ side were due to host Rennes at the Stade Velodrome at 8pm GMT, but that game is now off after ugly scenes that transpired just hours before kick-off.
Local police said that 300 supporters “violently attacked” officers during the protests against the club’s ownership, with 25 arrests made.
TV pictures showed fans forcing their way in and some were seen throwing flares and lighting firecrackers.
“Given the incidents that occurred this afternoon at the Olympique de Marseille training centre, the Marseille v Stade Rennais Ligue 1 match is postponed,” the French League (LFP) said in a statement.
French outlet RMC Sport published footage of fans marching in the streets and carrying banners reading “(Club) directors, out”, and others directly targeting Marseille president Jacques-Henri Eyraud.
Marseille are currently seventh in the Ligue 1 standings after losing each of their last three matches, 16 points adrift of leaders Lyon, with Villas-Boas hinting that he will leave the club when his contract expires in June.