Ponting arrived home last week for treatment for the left thumb fractured while fielding in Australia's six-wicket loss to England in the ICC Champions Trophy semi-final at Edgbaston.
CA said Ponting would now also miss the second Madras Test following a review of his fractured thumb by a hand specialist here on Thursday.
CA medical officer Trefor James said Ponting was making good progress but required further examination and would not be fit to play in the first two Tests of the four-match series.
"The bone seems to be repairing well and there has been no change in the status of the injury," James said in a statement.
"Ponting will visit the specialist again on October 14, and with the injury progressing at its current rate, we expect he'll be available for the third Test in Nagpur."
The much-anticipated series gets underway in Bangalore on October 6.
The Australian tourists will be led by wicketkeeper Adam Gilchrist in Ponting's absence with Darren Lehmann named as team vice-captain.