Lyon have warned an "even more serious tragedy" could occur if action is not taken after manager Fabio Grosso was "seriously injured" in an attack on the team's bus in Marseille.
The Ligue 1 match was postponed after the Lyon bus was hit by rocks on its way to Stade Velodrome on Sunday.
Lyon said Grosso and assistant Raffaele Longo were struck by projectiles and had sustained facial injuries.
Marseille said it "deplores the unacceptable incidents".
Six visiting supporter coaches were also targeted before the game between 10th-placed Marseille and bottom-of-the table Lyon, which had been due to kick off at 19:45 GMT.
In a statement, Lyon said it "regrets that this type of situation occurs every year in Marseille", adding the club "invites the authorities to take stock of the seriousness and repetition of this type of incident before an even more serious tragedy occurs".
According to the club, several individuals "violently attacked" the team bus and windows were smashed by projectiles.
Images on social media showed a bloodied Grosso lying on a stretcher. Lyon said the manager and his assistant were "directly hit and seriously injured in the face during the attack".
The visitors initially wanted to carry on and play the match, but opinions changed following news of the injuries to Grosso and Longo - while the players' mental state was also taken into account.
"[Grosso] can't hold a conversation, he had shards of glass in his face," Lyon club president John Textor told Prime Video.
"I'm very angry - our players, our coach, prepared for tonight and the fans wanted to see the game played."
Textor added: "Once the window was broken, other projectiles hit him, just above the eye. There were beer bottles, which hit him on the forehead."
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