Medvedev broke Sonego at the first attempt and then twice more in the second set to reel off his 25th win in his past 26 tour-level matches.
"Every match is a struggle (on clay), but I have had some good matches on clay," said Medvedev. "I managed to play good against a very strong player on clay."
"It's completely different on clay, but confidence is confidence," the third seed added.
"It's about winning matches, because it is always two players that play, and one is going to win... I hope to bring this confidence even further."
Medvedev earned his tour-leading 30th victory of the season and will face Zverev in the last 16 - a first meeting between the pair on clay.
"We've had some tough matches," said Medvedev, who has won seven of 13 previous matches against Zverev.
Zverev is still finding his way back after tearing ankle ligaments in the French Open semi-finals last year against Rafael Nadal.
Following a difficult first-round tie against the dangerous Alexander Bublik, he beat Spain's Roberto Bautista Agut 6-4, 6-4 on Wednesday.
"I saw him (Zverev) in the first two matches, he seemed to be in good shape. I'm just going to have to be at my best," said Medvedev.
Ruud revenge
Casper Ruud, coming off a title in Estoril last weekend, kicked off his Monte Carlo campaign with a 7-5, 7-6(1) win over Botic van de Zandschulp.
"It is never easy to start at a new tournament and against a player I have lost to before," said Ruud, who avenged his early exit at the hands of Van de Zandschulp in Miami.
"Sometimes it is a little tricky playing someone you recently lost to, like 'Not again', but in this case I was a bit happy because I felt like some unfinished business from the Miami match."
Ruud, a semi-finalist in the Principality two years ago, will take on Jan-Lennard Struff next after the German knocked out 14th seed Alex de Minaur 6-3, 6-2.
Danish teenager Holger Rune swept aside two-time French Open runner-up Dominic Thiem 6-2, 6-4, while Jannik Sinner advanced as Diego Schwartzman retired while trailing by a set and a break.
Karen Khachanov, the ninth seed, downed Ilya Ivashka in straight sets to book a showdown with Andrey Rublev.
Novak Djokovic plays Italian youngster Lorenzo Musetti on Thursday for a place in the quarter-finals.
Musetti, who famously led Djokovic by two sets at Roland Garros in 2021 before being forced to retire, thrashed qualifier Luca Nardi 6-0, 6-0.
World number one Djokovic is appearing at his first tournament since failing to get a waiver to enter the United States for last month's Indian Wells and Miami events due to his anti-Covid vaccination stance.
US eighth seed Taylor Fritz overcame 2014 Monte Carlo champion Stan Wawrinka 7-6(10), 6-2.
Chile's Nicolas Jarry will take on two-time defending champion Stefanos Tsitsipas after outlasting Australia's Alexei Popyrin in three sets.
