Mbappe could also miss PSG's Ligue 1 opener against Lens on Thursday and Leonardo claimed the FFF showed a "lack of respect" to the French champions.
"I find it completely unacceptable that we learn from the press that one of our players is positive," he told RMC.
"They released a statement and sent the player home but no one from the federation has communicated this to us. No one has contacted us.
"Are we managing? Everyone gives lectures to PSG, that we're poorly managed. But when this happens, it's still PSG that have to manage the problems, despite not knowing about them.
"PSG are always the bad guys in the story. It is a lack of respect to never communicate with the club. We did not speak with anyone.
"We only spoke with Mbappe. We were the ones who had to put the pressure on. It is unacceptable."
Mbappe becomes the latest PSG player to return a positive test ahead of the new season.