The Frenchman was named in the starting lineup for the match at Stade de la Mosson.
He had a golden opportunity to give his side the lead in the eighth minute when PSG were given a spot-kick.
Mbappe took responsibility with Neymar not on the pitch.
What transpired over the next few minutes were almost unbelievable.
Mbappe saw his penalty brilliantly saved by Montpellier goalkeeper, Benjamin Lecomte.
However, Mbappe was given a chance to redeem himself when VAR ruled that Lecomte had come off his line.
The 23-year-old stepped up once more but, incredibly, his effort was well saved again by Lecomte.
The ball bounced off the post and fell to Mbappe, who looked almost certain to hit the back of the net from a few yards out.
But Mbappe got his effort horribly wrong and sent the ball well over the bar.
It was an extraordinary sequence of events and you can view it below…