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.
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.
"The time taken over the decision is incomprehensible," Lyon president Jean-Michel Aulas told Amazon Prime.
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.
An individual was arrested and taken into custody after being identified by stadium security cameras, police told the press.
Payet, the Marseille captain, was also hit by a bottle during a game at Nice in August. He had been heckled by Lyon supporters while warming up before kick-off.
Nice were docked a point after the incident with Marseille, who on Wednesday were ordered to play their next home game behind closed doors after trouble during last month's clash with Paris Saint-Germain.
The game between Nice and Marseille was halted with 15 minutes left and replayed in its entirety two months later on neutral ground in Troyes and without fans.