Neymar's 76th-minute penalty settled the friendly at Emirates Stadium on Saturday (AEDT), but a late challenge on the Brazil captain by his club-mate left him writhing in agony.
As he kept possession on the left flank, Neymar was hacked down by Cavani with a clumsy tackle that earned the Uruguay striker a yellow card.
The pair exchanged words after Cavani had helped Neymar back to his feet, leading to some suggestions there could be tension in Paris after the international break.
Mbappe insists there will be no problems, though, having already shared a joke with Neymar on WhatsApp.
"Cavani is a great player," Mbappe said. "He is really good for PSG.
"What happened with Neymar is... I sent a message on WhatsApp to Neymar with the video. And he laughed. So it is nothing.
"It was a duel, they defended their country, they were right to do so. Both of them gave their best.
"And it won't have any consequence in PSG, they will still hug each other and score goals together. So there is no problem."