The Frenchman, seeded five, had no answer to left-hander Muller's swinging serve as he bowed out 6-4 6-4.
Top seed and five-times champion Andy Murray, French Open runner-up Stan Wawrinka and 2016 Wimbledon runner-up Milos Raonic suffered surprise defeats on Tuesday.
Former champion Grigor Dimitrov was also in trouble when he lost the first set to French veteran Julien Benneteau but the sixth seed recovered to win 4-6 6-3 6-4 in one of the best matches of the tournament.
The Bulgarian gifted away an early break with a spate of double faults to give 35-year-old Benneteau the impetus.
But a superb lob followed by a Benneteau double-fault allowed Dimitrov to forge ahead in the second set and he was always in control thereafter, pulling off some crowd-pleasing diving volleys as he moved to victory.
"I started with three double-faults which is unlike me but I fought my way through the match and was composed," Dimitrov, who won the title in 2014, said.
Tomas Berdych was also given a testing workout against Canadian tyro Denis Shapovalov, who pushed the former Wimbledon finalist all the way before succumbing 7-6(4) 6-7(4) 7-5.
Shapovalov won junior Wimbledon last year and the 18-year-old showed his grasscourt potential against Berdych until the seventh-seeded Czech put away a rasping forehand on matchpoint to break for the first time.
The 34-year-old Muller won the grasscourt title in Den Bosch on Sunday and has continued that form on the London lawns.
With on-court temperatures nudging 40 degrees Celsius, Tsonga looked as listless as the sweltering crowd as Muller dominated behind his serve to claim his second title of the year, having never won one before.
He needed one break in each set to subdue former runner-up Tsonga and will face either Murray's conqueror Jordan Thompson of Australia or American Sam Querrey in the quarter-finals.
"It's working well for me at the moment," Muller, who saved all three break points he faced, said. "My serve is working great and it's good at this time of the year on the grass."
American Donald Young also progressed, beating Serbia's Viktor Troicki in straight sets.
(Reporting by Martyn Herman; Editing by Gareth Jones and Ed Osmond)
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