The 31-year-old played in the first test against New Zealand in Wellington but was ruled out of the second match in Christchurch due to back problems.
Siddle, who has played 61 tests for Australia and taken 208 wickets, returned to Melbourne on Monday for scans.
"Unfortunately those scans have indicated a stress fracture in his lower back," Cricket Australia physio David Beakley said in a statement. "He will now require a significant amount of time away from the game with a lengthy rehabilitation process.
"Whilst he is laid off with his current back injury, we will take the opportunity for Peter to have exploratory surgery on his left ankle to investigate and treat the cause of his ongoing ankle pain.
"Once that surgery is complete we will have a better idea of his prognosis and likely rehabilitation time frame."
(Writing by Sudipto Ganguly in Mumbai; Editing by Ian Ransom)
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