Petkovic had a scan after her straight-sets loss to Poland's Agnieszka Radwanska in Tuesday's second round of the Sydney International.
The German becomes the second top women's player to pull out of the year-opening Grand Slam following American Venus Williams' exit earlier this week with an autoimmune disease.
"I've been having some back problems for the last three or four months," Petkovic said in a WTA statement.
"I've been struggling with it, but I've always believed it was going to be fine and so I pushed through the pain.
"The last two weeks in Australia I've been having bigger problems and I could only play for 30-45 minutes without pain."
Petkovic said Tuesday's scans detected a stress fracture in her lower back.
"The only thing I can do right now is rest and hope that the bone will heal as fast as possible," she said.
Petkovic said she had been advised her recovery could take between six to eight weeks.
"I'm positive this is going to be fine. I just need to take the time off to get better," he said.
"With this type of injury I'd rather take an additional week off, than start back a day early, and I need to be patient."
Petkovic said she will return to Germany later Wednesday to undergo further tests.
