Marseille's players were warming up before their UEFA Europa League match with Vitoria Guimaraes in Portugal when Evra was targeted by supporters with unkind chants.
Evra responded by vaulting the advertising boards and confronting the fans, who made their way down from the stands and approached the player.
The defender was carried back over the hoardings by a team-mate, before then aiming a kick at a Marseille fan's head and being dragged away again.
Evra was sent off as a result, becoming the first player to ever receive a red card before kick-off in a Europa League match.
Marseille confirmed after the game they had opened an investigation into the incident, while UEFA also began disciplinary proceedings against Evra and said that will be suspended for at least one match.
Now it appears his future at the club is in doubt, with Marseille revealing they have suspended him and will hold a meeting in due course to determine any further sanction.
A statement on the club's website read: "Jacques-Henri Eyraud, President of Olympique de Marseille (OM), met Patrice Evra today and informed him of his layoff with immediate effect and his summons to an interview prior to a possible disciplinary sanction.
"In addition, the first results of the internal investigation conducted by the club reveal an unacceptable behaviour on the part of a handful of provocateurs who uttered particularly serious hateful attacks against the player, even though the latter and his team-mates warmed up for an important meeting.
"As a professional and experienced player, Patrice Evra could not respond in such an inappropriate way.
"The club is continuing its investigation and will use all the legal means at its disposal against individuals who, under the guise of their passion for OM, endanger their reputation by entering the field and insulting a player instead of supporting him."
The UEFA disciplinary body will meet on November 10 to rule on the incident.