Mbappé spent five years at AS Monaco before leaving for Paris Saint-Germain, and said on the eve of this reunion that the Ligue 1 club had helped achieve his dream of being a professional footballer.
But there was no room for sentiment as Mbappé struck twice in the opening 26 minutes to boost Real's hopes of a top-eight finish in the league phase.
Franco Mastantuono, a Thilo Kehrer own goal, Vinícius Júnior and Jude Bellingham completed the rout as Alvaro Arbeloa's first Champions League game turned into a stroll.
Jordan Teze grabbed a consolation goal for Monaco in the final quarter after Real were caught out attempting to play from the back.
Arbeloa's first game after succeeding Xabi Alonso had ended in embarrassment with a Copa del Rey defeat to second-tier Albacete.
But Real, who bounced back with a league win over Levante on Saturday, were ahead after five minutes when Mastantuono found Federico Valverde, who helped it on to Mbappé.
The finish from just inside the box was precise as Mbappé stroked it beyond goalkeeper Philipp Köhn and into the corner of the net.