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The 30-year-old had been set to return to competitive action this week having been sidelined since Wimbledon due to hip problems.
But a statement on the tournament's website on Tuesday morning said the British number one had pulled out "due to pain in his right hip".
Murray, who remains registered for the Australian Open in Melbourne on January 15, will remain in Brisbane "as he works towards returning to the tennis circuit", according to tournament organisers.
The former world No 1 is the latest big name to drop out of the Brisbane event after Rafael Nadal confirmed in December that he would have to miss the tournament due to his continuing knee problem.
Both men face a battle to be fit for the first Grand Slam of the year, where defending champion Roger Federer has already been installed as a firm favourite.
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“I started to feel a bit better towards the end but I’ll need to keep improving, for sure”
Andy Murray
Murray and Nadal have both pulled out of tournaments this week while Novak Djokovic, who missed the same amount of time last year as Murray, had to withdraw from the Mubadala World Tennis Championship on medical advice after experiencing further pain in his troublesome elbow.
But 30-year-old Murray appeared confident of making it to the Australian Open in one piece when speaking after his exhibition set last week.
“When you haven't competed for a while, it takes time to get up to that pace,” Murray said.
“I started to feel a bit better towards the end but I’ll need to keep improving, for sure.
“It was nice. I was planning on stopping here for a couple of days on the way over to Australia to get some practice in with the guys here.
“It was unfortunate that Novak was unable to play so I agreed to play a set. “I was very lucky to be able to come out here and play in front of everyone.
“It was good fun. I’ve missed it.”