PSG won the match 4-2, but it was marred late on by Mbappe's first Ligue 1 dismissal, as he grew frustrated with some rough treatment.
The France international darted beyond Savanier on the break, before being cynically scythed down.
Mbappe reacted by running over to the Nimes man and pushing him to the ground, with both men subsequently sent from the field.
The World Cup winner apologised to the PSG fans after the game, saying that he "ruined our excellent team success".
PSG Thomas Tuchel came to his defence, saying that the 19-year-old was reacting to "a horrible foul".
He added: "He was lucky not to be seriously injured. I want him to stay calm but in a match like that, in an atmosphere like that, it's not easy. He didn't hit somebody, he just pushed."
But Savanier had a different perspective, as he predicts the young sensation will be on the receiving end of many more red cards after Mbappe said he would react the same way if the incident occurred again.
“I didn’t see it coming. I was surprised when he reacted like that," he said.
"If he continues like this, he’s going to see a lot of red cards this season."
His first game back in the French top flight will be against Nice on September 29.