Payet required treatment after being struck on the side of the head as he prepared to take a corner in the fifth minute, prompting both teams to return to the changing rooms.
Marseille president Pablo Longoria called it a “dark night for football”.
“Dimitri is affected psychologically, it’s not normal,” he told Amazon Prime.
“We always condemn any kind of violence, it affects everyone. Nobody who likes football can be happy tonight. The impact was a bit violent, he was very affected, with ice on his head in the dressing room.”
It was the latest in a series of incidents that have blighted French football this season and confusion reigned after an initial decision was made to resume the game following a 90-minute delay.
“Contrary to what was announced, the referee has decided not to restart the game given the security of the players was not guaranteed,” the stadium announcer said.
Lyon players initially came back out to warm up following an announcement that play would restart, but soon headed back down the tunnel with no sign of their opponents.
“My decision from a sporting perspective was always to not restart the match. Public order disturbances were mentioned,” said referee Ruddy Buquet.
“The time taken over the decision is incomprehensible,” said Lyon president Jean–Michel Aulas.
French league officials said they “regretted” the decision to try and restart the match. The LFP’s disciplinary committee will hold an emergency meeting on Monday.