The victory, in just over two and a quarter hours on Friday, marked another disappointment for Murray, who has not won a title since his historic success at Wimbledon 13 months ago.
The 27-year-old Tsonga's highlights this season have been limited to a pair of semi-finals, at Acapulco and Roland Garros.
Murray, who led 3-0 in the deciding set, had not played this week since the second round after receiving a walkover when Richard Gasquet withdrew from their scheduled third round clash with an abdominal strain.
"It's just disappointing because it's important to play matches," said Murray, still trying to lift his form after back surgery 10 months ago and playing his first event since Wimbledon a month ago.
"If you've had a break for a while, ideally you want to try and play as many matches as you can. Tennis and sport really can change a lot from one day to the next. Jo is a top player. He's a fantastic athlete. When his game is on, he's very tough to beat,” he added.
It was the second upset of a top 10 player in as many days for Tsonga, who knocked out world number one Novak Djokovic in the third round.
Tsonga, seeded 13th, stood 1-9 in his career head-to-head series with world number nine Murray, whose ranking is at its lowest since 2008.
The Frenchman will next play Grigor Dimitrov after the seventh seed beat South African Kevin Anderson 5-7 7-5 7-6 (8/6) in a match lasting three hours.

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