Mbappe, 18, became the youngest player to score three times in one French top-flight match since a 17-year-old Jeremy Menez in 2005, while the in-form Radamel Falcao added a double to keep second-place Paris Saint-Germain at bay.
Mbappe, who has been linked with a move to Arsenal and recently compared to Thierry Henry by Gunners manager and former Monaco boss Arsene Wenger, fired home the opener after Falcao's cushioned header, and the Colombian added the second in the 10th minute with a near-post finish from Almamy Toure's cross.
Monaco continued to dominate and Mbappe scored his second with a powerful strike after cutting inside from the left, and he completed his hat-trick with a lovely dink over the onrushing Thomas Didillon.
3 - @KMbappe is the youngest player to score a hat-trick in Ligue 1 (18 yo & 2 mo) since Jérémy Menez in 2005 (17 yo & 8 mo). Promise.— OptaJean (@OptaJean) February 11, 2017
The victory was soured by Gabriel Boschilia being taken off on a stretcher after sustaining what could be a serious knee injury in the second half.
Boschilia's throughball was key, but the young Brazilian was unable to see out the match after a challenge with Jonathan Rivierez saw him spin awkwardly on his knee.
Monaco had done enough to move clear of PSG at the top, with the result meaning they have scored 12 unanswered goals against Metz this season.