"Follow-up scans have confirmed that he has bone oedema in his vertebrae," CA's support team physiotherapist David Beakley said in a statement.
"It is important that Pat has time off bowling, to prevent the injury becoming more serious and consequently we have made the decision to rule Pat out of the IPL.
"Pat will now undergo a period of recovery and rehabilitation and we will look to re-scan him in a few weeks to assess the healing.
"Following this we will be in a better position to decide on Pat's return to play timeline including participation in the limited overs tour of the UK."
Cummins has played 13 consecutive tests for Australia since being called up during the tour of India last year.
The 24-year-old was part of the side that scored a 4-0 Ashes series win against England and he claimed 22 wickets in four tests in South Africa.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
