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The 33-year-old fell at the semi-final stage of the exhibition tournament as British number one Dan Evans came back to win 1-6 6-3 10-8 on Saturday.
Murray was due to face Cameron Norrie on the exhibition's final day, but has withdrawn from the competition as a precautionary measure.
Murray, who did not wish to aggravate his niggling injury further by playing five matches in six days, will still be on court to coach his replacement James Ward.
The Scot has won two of his four matches at the tournament and took a set off Evans and British number two Kyle Edmund.
Murray is set to prepare for the US Open by competing in Washington when the ATP Tour resumes in August and has also said he is prioritising Grand Slam events.
Evans faces Edmund in Sunday's final.
Alexei Popyrin coasts past Benoit Paire at UTS
Quarter-finals, Day 1