Samuel Moutoussamy put the hosts ahead before Myron Boadu levelled to send the game to penalties.

Moses Simon netted the decisive kick after Wissam Ben Yedder and Aurelien Tchouameni missed their efforts for Monaco.

Nantes, who last won the cup in 2000, will play Nice at the Stade de France on 8 May.

Nice, who knocked out Paris St-Germain in an earlier round, beat fourth-tier Versailles 2-0 on Tuesday.

This will be the first French Cup final without PSG since 2014. They won six of the past seven finals.