Evra was sent off in the warm-up prior to Marseille's Europa League tie with Vitoria Guimaraes after his talk with fans behind the advertising hoards escalated into an attack against one supporter.
The Ligue 1 club said that they would interview the former Manchester United player before deciding on a punishment, but released a statement on the incident.
"Jacques-Henri Eyraud, president of Olympique de Marseille, met Patrice Evra and informed him of his suspension with immediate effect and his summons to an interview prior to a possible disciplinary sanction," the statement read.
"The first results of the internal investigation conducted by the club reveal unacceptable behaviour on the part of a handful of provocateurs who uttered particularly serious hateful attacks against the player, as he and his teammates warmed up for an important game.
"As a professional and experienced player, Patrice Evra could not respond in such an inappropriate way."
Marseille lost Thursday's tie 1-0 but remain second in group I with two games remaining in the group stages.