Murray, playing in his first tournament since losing his fourth Australian Open final, was unusually profligate, committing numerous unforced errors from his usually rock-solid groundstrokes.
The Scot slipped 5-1 behind in the first set before playing some of his best tennis to break back once, but eighth seed Simon held firm to take the opener in Rotterdam.
Simon continued to outmanoeuvre Murray in the second set and forged 4-0 ahead before the Briton again offered some stiff resistance, threatening to get back to 4-3.
In other quarter-finals, Milos Raonic of Canada beat Sergiy Stakhovsky of Ukraine 2-6, 6-3, 6-4 and fourth seed Stanislas Wawrinka of Switzerland) got the better of Gilles Muller of Luxembourg 7-6(3), 6-3.
Image: Giles Simon
Photograph: Zhong Zhi/Getty Images
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