The former world No 1 lost in straight sets to Matteo Berrettini. The Italian, who is the top seed, won 6-3, 6-3.
Murray, a record five-time winner of the singles at Queen’s Club, was always up against it in the second-round tie against the world No 9.
The Scot, back on the comeback trail following yet another injury setback, was playing in his first grass-court singles tournament since 2018. He defeated France’s Benoit Paire in the first round but Berrettini proved a far tougher foe.
The Italian will face Britain’s Dan Evans in the last eight. Evans reached his first Queen’s quarter-final with a 6-4, 7-6 (7) victory over France’s Adrian Mannarino.
Murray must now regroup ahead of Wimbledon which begins on June 28. The two-time champion has received a wild card for the All England Club.
Murray’s movement against Berrettini did not seem to be impaired by his recent groin problem. But the 6ft 4in Italian, with one title under his belt already this season, regularly boomed down serves of 140mph and secured a first-set break for 3-2 when the Scot wafted a forehand long.
Murray faced two set points on his own serve and surrendered the second when he dumped a forehand low into the net.
The 34-year-old had a chance to claw back an early break in the second but was unable to take advantage as Berrettini moved 3-0 ahead.
And Murray’s bid to reach a seventh Queen’s Club quarter-final, and a first since he won the title in 2016, ended when Berrettini ruthlessly held to love.