Fekir took off his shirt, brandishing his name and number to St Etienne fans, after scoring Lyon's fifth five minutes from time of their 5-0 triumph over their bitter Rhone rivals.
Angered by the gesture, which has also been employed by Barcelona's Lionel Messi and Cristiano Ronaldo in the past, St Etienne supporters spilled onto the pitch, forcing a 40-minute stoppage before the teams could play out the final five minutes in a virtually empty Stade Geoffroy-Guichard.
It was the second stoppage referee Clement Turpin had been forced to call after a shorter halt to proceedings early in the game due to smoke from flares lit by home fans, making visibility difficult.
"No, I don't regret what I did," Fekir said afterwards. "It's true, it's perhaps a gesture that they didn't like. I celebrated my goal like that. There was nothing behind it, no nastiness. Perhaps it wasn't the right thing to do. It was 5-0, but it's just football. It also added a little bit of spice."
L'Equipe reported on Monday that the French Football League (LFP) will open an investigation into the incidents, including Fekir's goal celebration, when its Disciplinary Commission sits on Thursday.
The body could decide to punish Fekir, who will team up with the France squad on Monday ahead of their upcoming friendlies with Wales and Germany.
Lyon coach Bruno Genesio lent his support to the midfielder.
"I think it was perhaps a bit out of place, but I don't think there was any nastiness or provocation on Nabil's part," Genesio said. "I know him well enough to know he's a very respectful person. I think the context of the game made him celebrate his goal in that way.
"I don't expect any punishment. You have the right to celebrate goals. You don't have to invade the pitch because a player celebrates a goal. Otherwise we'll have to stop playing football. It's the essence of football to score goals, to bring joy to your teammates, the staff, the fans. I don't see why he would be punished."
Lyon's Portugal international goalkeeper Anthony Lopes added: "There will be negative opinions, positive opinions. He celebrated his goal as he wanted. Now we'll see what happens.
"We can't go on and on about it too long. You can ask Lionel Messi and Cristiano Ronaldo -- they did the same celebrations."