The Lyon bus was hit on the way to Stade Velodrome, shattering some windows. Grosso was injured by falling shards of glass and needed medical treatment with his face heavily bleeding.
SkyItalia broadcast video footage showing damage to the bus, sustained as it headed towards the stadium, as well as Grosso being led away by personnel while bleeding and covering his face.
It wasn't clear less than an hour before kickoff whether French league officials would let the game be played in such circumstances, but the Ligue 1 fixture was eventually called off shortly after it was supposed to have started.
There are no confirmed reports as yet over who was responsible for attacking the Lyon team bus.
Marseille have a recent history of incidents involving their stadium or supporters, including fans storming the training ground and setting a fire, enforcing a match being postponed in 2021. The Metropolitan Police arrested five people a year ago, “believed to be away supporters,” when Marseille played a Champions League game at Tottenham. And one Marseille fan faced an attempted murder charge over firing a flare into Eintracht Frankfurt fans at a game, seriously injuring one visiting supporter.
Lyon manager Grosso scored the winning penalty kick for Italy in the shootout victory over France in the 2006 World Cup final.
Both clubs have been under pressure lately. Despite replacing Marcelino with Gennaro Gattuso as coach in September, Marseille remain showing poor form with one win and three losses in their last four league games. Lyon are the only team still winless in the league. Replacing Laurent Blanc with Grosso as coach in September hasn't paid off for Lyon, as they sit in last place.
Additional reporting by Associated Press