The three-time Grand Slam champion, who dislodged Novak Djokovic from the top of the rankings towards the end of 2016, has slipped to 19th in the world due to his lengthy lay-off.
Murray's withdrawal comes amid a string of injury concerns that have plagued some of the world's top players and cast doubt on their participation first Grand Slam of the year, which is due to begin in Melbourne on January 15.
Murray said on Sunday he felt in great shape and that he was confident he would play in Brisbane. But the 30-year-old Scot issued a statement Tuesday announcing his withdrawal from the tournament
Murray is due to face world number two Roger Federer in a charity exhibition match in Glasgow on Tuesday before he starts his preparations for the Australian Open by playing in Brisbane.
The 31-year-old became the oldest man to secure top spot in the end of season rankings.
Murray has been struggling with the hip injury since a five-set French Open semi-final loss to Switzerland's Stan Wawrinka in June.
Andy Murray, a three-time Grand Slam champion whose first major title came in 2012 on the New York hardcourts, was uncertain about his status for the remainder of the season.
Will Roger Federer's style - the variegated and beautiful all-court approach - live on in the next generation?
Rafael Nadal had slipped to as low as 13th in the ATP rankings midway through 2015.
Roger Federer attributed his renaissance to rediscovering full fitness after knee surgery in 2016 and taking a two-month break from the game earlier this year.
A semi-final run in Montreal would see the Spaniard supplant Britain's Andy Murray atop the rankings.
World No. 1 Andy Murray has a history of standing up for equality in professional tennis.
Sam Querrey sent defending champion Andy Murray crashing out of Wimbledon on Wednesday, reaching his first Grand Slam semi-final at the 42nd attempt.
Third seed Federer reached his 50th Grand Slam quarter-final and 15th at Wimbledon with a 6-4, 6-2, 6-4 win over Grigor Dimitrov.
Defending champion Andy Murray added his voice to the growing list of unhappy players.
Murray needed only 96 minutes to see off the dreadlocked German on Centre Court.
Venus Williams wept at Wimbledon over the "devastation" of a fatal road accident for which she is facing legal action as Andy Murray and Rafael Nadal eased into the second round on Monday.
Andy Murray said knowing he is due to become a father again wouldn't provide extra inspiration as he chases a third Wimbledon title and fourth Grand Slam crown.