Sky Italia footage showed damage to two bus windows and Grosso being led into the stadium by two assistants. He was covering his face with his hands, which were stained with blood.
Italian media said Grosso suffered injuries to his scalp and face.
"He can't hold a conversation, he had shards of glass in his face," Lyon's club president, John Textor added.
"I'm very angry - our players, our coach, prepared for tonight and the fans wanted to see the game played," he told Prime Video.
Fans were asked to leave the stadium calmly.
"Following the injuries of Lyon members, considering the opinion of the club, which did not wish to start the match, and the established protocol, the decision was taken not to play the match," said referee Francois Letexier, quoted by French media.
There was no immediate official announcement regarding plans for the game.
