Grosso, a World Cup winner with Italy in 2006, sustained facial injuries during the incident, leaving league officials to deal with another episode of rioting fans.
Some preliminary round Olympic matches will be played in Marseille, where violence erupted at the 1998 World Cup between England fans and French police.
Marseille condemned the behaviour of their fans in a statement on Monday.
Lyon condemned their fans' behaviour after some were seen making Nazi salutes at the Velodrome.
"OL firmly condemns the unacceptable racist behaviour of individuals in the stands on Sunday," the club said in a statement.
Persons:
Lyon, Fabio Grosso, Gerald Darmanin, Pablo Longoria, Marseille, Amelie Oudea, Castera, St Etienne, Julien Pretot, Sudip Kar, Tassilo Hummel, Michael Perry
Organizations:
Olympique de Marseille's Ligue, Olympique Lyonnais, Italy, Marseille's Stade Velodrome, French League, England, French, Olympique de Marseille, Stade Orange Velodrome, France, Stade Velodrome, Marseille, RC Lens, Lille, St, Thomson
Locations:
Grosso, Marseille's, Marseille, Nice, Montpellier, Angers