The Scot had pulled out of the Rogers Cup with the same injury, which also hampered July's Wimbledon campaign.
The 30-year-old is now certain to lose his number one ranking this month and is a doubt for the US Open, which starts on 28 August.
"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."
The US Open - the final Grand Slam of the season - runs until 10 September in New York.
Murray, who has held the number one ranking since November, will be overtaken by Rafael Nadal on 14 August if the Spaniard reaches the semi-finals of the Rogers Cup in Montreal this week.
If not, either Nadal or Roger Federer will replace Murray at the top of the standings after Cincinnati on 21 August.
World number one Andy Murray has withdrawn from the Cincinnati Masters because of an ongoing hip injury.