Mbappe opened the scoring with an early penalty and then grabbed a second goal just before half-time after being set up by Lionel Messi to get his 100th goal in France's top flight since moving to PSG in 2017.
The France striker, who also scored 16 league goals for Monaco at the beginning of his career, does not turn 23 until later this month.
The victory allowed PSG to extend their lead at the top of Ligue 1 to 13 points from Marseille, who won 2-0 at Strasbourg earlier on Sunday and have a game in hand.
Mauricio Pochettino's side ultimately eased to victory in a subdued atmosphere at the Parc des Princes, with one end of the stadium closed as a punishment after the club's ultras let off flares en masse during a recent game.
Monaco had lost just twice in their previous 12 visits to Paris in Ligue 1 and were the better side in the first half, but Mbappe's second goal right on the stroke of half-time was a hammer-blow from which they did not recover.
Niko Kovac's team are eighth, five points adrift of the top three, with just one more round of games to come before France's short winter break.
Sofiane Diop hit the post for the principality outfit inside two minutes but they soon found themselves behind.
Angel Di Maria went down in the box and the referee spotted a foul by Djibril Sidibe after a review of the images. Mbappe stepped up to convert the penalty.