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The victory helped Tsitsipas join Rafael Nadal as the only active player to win consecutive titles at Monte Carlo, with the likes of Juan Carlos Ferrero, Thomas Muster, Bjorn Borg and Ilie Nastase also achieving the feat during their playing days.
It was the first time in 13 years that the 35-year-old Monfils beat the No.1-ranked player in the world.
Tournament organisers said in a statement that valid proof of full vaccination would be required for entry into the venue.
Nadal, playing in what is considered to be the greatest era of men's tennis, surpassed the haul of Roger Federer and Novak Djokovic on Sunday.
Should Medvedev defeat the Spanish great, he will become the first man in the Open era to win his first two Grand Slam titles in succession after his triumph in New York last September.
A win for Nadal in Sunday's final will break a three-way tie with Novak Djokovic and Roger Federer and give him sole owenership of the record for most Grand Slam singles titles.
World No. 2, Medvedev beat Felix Auger-Aliassime 6-7(4) 3-6 7-6(2) 7-5 6-4.
Immigration Minister Alex Hawke used discretionary powers to again cancel Djokovic's visa, after a court quashed an earlier revocation and released him from immigration detention on Monday.
"A very small majority chose to follow their own way, which kind of makes the majority look like fools," Tsitsipas said.
The 25-year-old, who will make his second appearance at the ATP Finals, defeated Australia's Alexei Popyrin 7-6(3), 6-3 in the opening round of the Vienna Open.