The organisation's medical adviser Trefor James said a specialist's examination on Saturday confirmed Ponting had a fracture to the distal phalanx of his left thumb.
"After discussion with Ricky, we have decided he should rest for the next few days and we will organise a re-examination for later next week to check his progress and better assess when he might be able to grip a bat and field," James said in a statement.
"Fortunately, the specialist has advised that the bones are sitting well and surgery will not be necessary, but it is difficult at this stage to assess how long will be needed before he can resume playing.
"While it is difficult to assess, it is highly unlikely he will be ready to play by the time of the first Test starting at Bangalore on October 6."
Ponting arrived home on Friday from London for treatment for the thumb fractured while fielding in Australia's six-wicket loss to England in the ICC Champions Trophy semi-final at Edgbaston on Tuesday.
The Australian tourists have arrived in Mumbai, under stand-in skipper Adam Gilchrist, in preparation for their opening three-day game against Ranji Trophy champions Mumbai at the Brabourne Stadium on September 30.
There are four Tests in Bangalore, Chennai, Nagpur and Mumbai.