The Marseille captain required treatment after being struck on the side of the head as he prepared to take a corner for the visitors in the fifth minute of Sunday's match at Lyon's Parc OL stadium, prompting both teams to return to the changing rooms.
Payet, who did not train on Monday, has lodged a complaint with the Lyon public prosecutor investigating the incident, a Marseille club official told AFP.
The French professional football league (LFP) said that "in light of the serious incident that occurred during the match", its disciplinary committee had opened an investigation and, as a precaution, ruled that all games at the Parc OL stadium be played behind closed doors until a ruling is made, which will not come before December 8.
It means there will be no fans for Lyon's home Ligue 1 match against Reims, scheduled on December 1. Lyon are away to Montpellier and Bordeaux in Ligue 1 action on November 28 and December 5 respectively, with a trip to Denmark to take on Brondby in the Europa League on Thursday.
France's Interior Minister Gerald Darmanin and Sports Minister Roxana Maracineanu will meet Tuesday with representatives from the LFP and the French football federation to see "what must be done".
It is the latest incident in a Ligue 1 season that has been rocked by incidents involving spectators.
An individual was arrested and taken into custody after being identified by stadium security cameras following the Payet incident, police told AFP.
Lyon added that the 32-year-old male protagonist was neither a member of a fan club nor a season ticket holder.
Payet 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.
Nice were also ordered to play three games behind closed doors. Lens incurred a similar punishment following a pitch invasion during September's northern derby against Lille.