Medvedev and Tsitsipas have been drawn in the opposite half of the tournament to 13-time winner Nadal, defending champion Djokovic as well as teen sensation Carlos Alcaraz.
"It's good from one side to have them on the other side of the draw. At the same time, me, even more than other tournaments, I have to focus on myself," said Medvedev.
"There are a lot of good clay court players. I'm playing one of them first round, lefty, likes to spin the ball."
Fourth-seeded Tsitsipas, who lost the 2021 final to Djokovic after leading two sets to love, has a dangerous assignment against Italy's Lorenzo Musetti in the night session on Court Philippe Chatrier.
The 20-year-old, ranked 66, also led Djokovic by two sets in the last 16 in 2021 before injury curtailed his challenge.
This year on clay he made the quarter-finals in Marrakech and third round at Monte Carlo, Barcelona and Madrid where he was forced to retire against world number three Alexander Zverev.
Two former women's champions also get their campaigns underway.
Simona Halep, the 2018 champion, who is working with Serena Williams's coach Patrick Mouratoglou, faces Nastasja Schunk, an 18-year-old lucky loser from qualifying, ranked at 165 in the world.
Jelena Ostapenko, who was a shock Roland Garros winner in 2017, faces Italy's Lucia Bronzetti.
Spain's world number four Paula Badosa, a quarter-finalist in 2021, takes on France's Fiona Ferro.
Before that match on Court Philippe Chatrier, French fans will possibly bid farewell to Jo-Wilfried Tsonga, the former world number five who will retire once his French Open campaign ends.
Tsonga, unseeded, lost the 2008 Australian Open final to Djokovic as the Serb claimed the first of his 20 Grand Slam titles.
He made it to the semi-finals twice at both the French Open and Wimbledon and finished runner-up to Roger Federer at the ATP Finals in 2011.
"It's a moment which I am sure will be full of emotion," said the 37-year-old who takes on eighth seed Casper Ruud, the champion in Geneva at the weekend.