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The three-time Grand Slam winner lost in straight sets 7-6 6-3 to Poland’s world no13 Hubert Hurkacz on Wednesday.
That was only Murray’s second contest since the Tokyo Olympics, where he was forced to withdraw from the men’s singles event due to a minor thigh strain.
He played in the men’s doubles competition in Japan alongside fellow Briton Joe Salisbury, losing to Croatian pair Marin Cilic and Ivan Dodig in the quarter-finals.
Murray - a champion in Cincinnati in both 2008 and 2011 - was later added to the main draw for the US Open, which begins on August 30 at New York’s Flushing Meadows, following the withdrawal of former winner Stan Wawrinka.
The 34-year-old impressed as he beat Richard Gasquet in straight sets 6-4 6-4 in the first round in Cincinnati on Tuesday, but could not repeat the feat against ninth seed Hurkacz.
Britain’s Heather Watson is also out of the Western and Southern Open following a 6-4 7-6 defeat by world no1 Ashleigh Barty.