Medvedev, who had never won a match at Roland Garros before this year, defeated Cristian Garin of Chile 6-2, 6-1, 7-5 in his last 16 tie.
Tsitsipas, a semi-finalist in 2020, eased past Spain's Pablo Carreno Busta 6-3, 6-2, 7-5.
Zverev downs Nishikori to reach French Open last eight
Alexander Zverev progressed to the French Open quarter-finals for the third time in four years on Sunday with a crushing 6-4, 6-1, 6-1 win over Japan's Kei Nishikori.
Sixth seed Zverev will face world number 46 Alejandro Davidovich Fokina of Spain for a place in the last four.
"I played incredible, I played a very good match but the tournament isn't over," said Zverev.
"I'm into the quarter-finals but I've hopefully got three matches left and we'll see how those go."
Zverev has won his past 12 sets at Roland Garros after recovering from two sets down against qualifier Oscar Otte in the first round.
"If I play my best tennis I'm difficult to beat," he added.
Zverev is the second German man in the Open era to reach three quarter-finals in Paris after Boris Becker (1986-87, 1989 and 1991).