The two-time Wimbledon champion is struggling to overcome the issue which hampered his progress ahead of Wimbledon last month.
Murray had been forced to miss training ahead of the event at SW19 and he eventually broke down during his defeat to Sam Querrey in the quarter-finals.
The Scot was able to finish the match but the injury forced him to miss this week's event in Montreal.
He could now lose his No.1 spot to Rafael Nadal but Murray is still hoping to compete at the US Open in New York later this month.
"Unfortunately 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.
"I'm continuing to work hard on the court with the aim of being in New York."