After world number one Andy Murray, three-time Grand Slam champion Stan Wawrinka and former Wimbledon finalist Milos Raonic all endured shock first-round defeats on Tuesday, it was Tsonga's turn to suffer a surprise second-round exit.
Fifth-seeded Tsonga is traditionally a powerful force on grass and finished as Queen's runner-up in 2011, while twice appearing in the Wimbledon semi-finals.
But the 32-year-old, who has won titles in Lyon, Marseille and Rotterdam in 2017, was out of sorts from start to finish against the big-serving Muller.
It took Muller just 69 minutes to hand Tsonga another frustrating loss on the heels of his embarrassing first-round exit against Renzo Olivo at the French Open.
"Sometimes you cannot do anything because the guy in front of you is doing the right things to make you play in a bad way," Tsonga said.
"I played two matches here. That's life. I'll try to play better in Wimbledon.
"I have to put a little bit more energy in my game."
Muller's impressive display maintained his recent surge, which has seen the 34-year-old win the 's-Hertogenbosch grass-court tournament last week and reach a career-high ranking of 26.
Muller is in the quarter-finals at the Wimbledon warm-up event for a third successive year and will play former Queen's champion Sam Querrey or Australia's Jordan Thompson for a place in the last four.
Grigor Dimitrov fought back to avoid becoming yet another big name casualty as the Bulgarian world number 11 defeated France's Julien Benneteau 4-6, 6-3, 6-4.
Dimitrov won Queen's in 2014 and, given the way the tournament has unfolded, the sixth seed must fancy his chances of claiming the title again.
The 26-year-old was pushed hard by the world number 87 in almost two hours on court in searing heat, but he battled through to set up a quarter-final clash with Australian wild card Thanasi Kokkinakis or Russia's Daniil Medvedev.
It is the first time Dimitrov has made the last eight of an ATP event since Rotterdam in February.
Donald Young reached the Queen's quarter-finals for the first time as the American world number 55 defeated Serbia's Viktor Troicki 6-3, 6-4.
Young, who arrived at Queen's on a five-match losing streak, faces former US Open champion Marin Cilic or American qualifier Stefan Kozlov with a semi-final berth at stake.