Johnson suffered the problem in Australia's tri-series against South Africa and Zimbabwe that concluded earlier this month.
The left-arm quick returned to Australia for treatment but it was expected that Johnson would feature in the Twenty20 tournament for Kings XI Punjab in the latter stages.
Cricket Australia announced on Friday that Johnson would not travel to India for the tournament, though, with the organisation's executive general manager of team performance, Pat Howard, confirming the decision.
Johnson will now travel to the United Arab Emirates with Australia's limited-overs squad on Sunday ahead of next month's series.
"Unfortunately, Mitchell is not back to 100 per cent fitness so we will not be releasing him to Kings XI Punjab for the remainder of the Champions League," Howard said.
"He will travel with the squad to Dubai on Sunday to continue his rehab with the team medical staff."
Australia will play one Twenty20 international, three one-day internationals and two Tests against Pakistan in the United Arab Emirates in October and November.