Seventh seed Tsonga, who celebrated his 32nd birthday on Monday, took the first set in a tie-break, but was broken five times as he lost the second and deciding set.
Mannarino claimed only the second top 10 scalp of his career, and will face Lucas Pouille or Paolo Lorenzi for a place in the quarters.
World number two Novak Djokovic is currently in action against Gilles Simon.
MEN'S SINGLES RESULTS
Adrian Mannarino (France) beat 7-Jo-Wilfried Tsonga (France) 6-7(3) 6-2 6-3
Carlos Berlocq (Argentina) beat Pierre-Hugues Herbert (France) 3-6 6-2 6-1
Jiri Vesely (Czech Republic) beat Mischa Zverev (Germany) 7-6(3) 6-3
Karen Khachanov (Russia) beat Nicolas Mahut (France) 6-2 6-4
Tommy Haas (Germany) beat Benoit Paire (France) 6-2 6-3
Paolo Lorenzi (Italy) beat Marcel Granollers (Spain) 6-2 6-4
Jan-Lennard Struff (Germany) beat Casper Ruud (Norway) 6-4 6-4
11-Lucas Pouille (France) beat Ryan Harrison (U.S.) 6-2 6-4
Robin Haase (Netherlands) beat Damir Dzumhur (Bosnia and Herzegovina) 6-3 6-2
Gilles Muller (Luxembourg) beat Tommy Robredo (Spain) 6-2 6-2
Read the original article on Eurosport: Mannarino upsets Tsonga in Monte Carlo