Murray has been in rehabilitation from the problem that ruined his Wimbledon campaign, but the tournament in Canada comes too soon.
His withdrawal casts further doubt on his fitness for the US Open, which begins later this month. Despite his struggles, Murray remains 9/2 third favourite for the US Open, which gets under way next month. In a sign of the times, the market is headed by the old guard with Roger Federer 13/8 and Rafael Nadal 100/30.
Murray said on the Rogers Cup website: "I am sad to be missing the tournament in Montreal because I have many great memories from my time in Canada.
"I am doing everything I can to return as quickly as possible."
Murray went into last month's tournament at SW19 carrying a hip problem and it was doubtful whether he would even be fit enough to defend the title he won in 2016.
He was visibly limping through games, but looked to be managing it until his quarter-final with Sam Querrey.
After taking the third set on a tie-break, Murray's body gave up on him and the American raced through the final two sets, with the Scot hardly able to move.
A leading hip surgeon said after his exit that he would be 50-50 to make Flushing Meadows, but hopes were raised after he posted a video of himself on Instagram tentatively hitting a ball against a wall.
It is the second year in a row he has pulled out of the Masters 1000 event in Canada - alternated each year between Montreal and Toronto - after missing it last year in preparation for the Olympic Games.
Tournament director Eugene Lapierre said: "We would have liked for Andy to be able to defend his title that he won here in 2015, but we wish him a very speedy recovery."
Murray is listed to compete at the US Open's final warm-up event - the Western & Southern Open in Cincinnati - starting on August 14 but there is no word yet on whether he will be there.
It means that next time he takes to the court he may no longer be world number one as Rafael Nadal closes in on his top spot.
The Spaniard is seeded first in Montreal and will return to the top of the rankings if he gets to the semi-final.
Murray joins Stan Wawrinka and Wimbledon runner-up Marin Cilic in pulling out of the event while Novak Djokovic will also be absent having confirmed he will miss the rest of the season due to an elbow injury.
