Murray withdraws from Cincinnati
The Scot also withdrew from this week’s Rogers Cup with the same injury.
“I’m continuing to work hard on the court with the aim of being in New York,” said Murray.
“I won’t be playing in Cincinnati as I continue my recovery – I always enjoy playing there and I look forward to returning next year.”
Murray is now a doubt for the US Open as well and could potentially join World No 4 Stan Wawrinka and No 5 Novak Djokovic on the sidelines for the final Grand Slam event of the year.
The 30-year-old could also soon lose the World No 1 spot to Rafael Nadal.
The Spaniard will take over at the top of the world rankings if he reaches the semi-finals of the Rogers Cup.
Nadal faces Croatia’s Borna Coric in his second round tie in Montreal later on Wednesday.
The US Open starts on August 28.