The match is scheduled to be held at the Sydney Cricket Ground from January 7-11.
"Fast bowler James Pattinson has been ruled out of our Australian squad for the third #AUSvIND Vodafone Test with bruised ribs," said Cricket Australia (CA).
A replacement has not been named for Pattinson, who got injured after a fall at home.
"He will not be replaced in the squad and will be assessed further ahead of the Brisbane Test match," CA added.
With Pattinson ruled out of the penultimate Test of the four-match series, Michael Neser has only Sean Abbott to compete with for a spot in the playing XI. The all-rounder was seen doing duty quite a few times as a substitute during the second Test in Melbourne.
Pattinson last played against India in a tour match in the lead-up to the opening Test of the series, picking up three wickets.
He has taken 81 wickets in 21 outings for Australia at an average of 26.33 and last featured in a Test against New Zealand last January.
The 30-year-old Pattinson was not included in the playing XI in the first two Tests and was unlikely to be a part of the third match as well, with Mitchell Starc, Josh Hazlewood, Pat Cummins and Nathan Lyon forming a four-pronged bowling attack.