The 30-year-old has been out of competitive action since last summer's Wimbledon but had been hopeful of featuring in the first Slam of the season, which starts in Melbourne on January 15.
Murray was already in Australia in the build-up to the Open and, having withdrawn from the Brisbane International last week, has now decided that he will return to the UK rather than risk competing.
"Sadly I won't be playing in Melbourne this year, as I am not yet ready to compete," he said in a brief statement.
"I'll be flying home shortly to assess all the options but I appreciate all the messages of support and I hope to be back playing soon."
Earlier this week Murray admitted that he is considering surgery in order to rectify the long-standing problem.