Callum Ferguson has been named Clarke's replacement in the ODI squad while George Bailey will lead the side. Bailey is also T20 skipper. Nic Maddinson has been added to the T20 squad.
Australia will play one Twent20 International and seven ODIs.
Last month, Clarke was named as skipper subject to proving his fitness ahead of the tour which starts on October 10 with the T20I.
Commenting on the changes, National Selector John Inverarity said: "Michael (Clarke) was very keen to captain the ODI team to India but unfortunately he hasn't progressed enough to be available for selection.
"His replacement is Callum Ferguson, whose form in 50-over cricket during the last Australian summer was impressive, scoring 271 runs at an average of 45 and a strike rate of 70 in the RYOBI CUP, along with an additional three matches for Australia A against the England Lions in February scoring 149 runs in three innings at 49.66 with a strike rate of 91.
"George Bailey will captain the ODI team in Michael's absence. Brad Haddin will be George's vice-captain.
"In addition, The NSP has added Nic Maddinson to the squad for the T20 fixture. Nic showed some sparkling form on Australia A tours during the winter.
"He will be in strong contention to open the batting with Aaron Finch in this game," Inverarity said.
Commenting on Clarke's injury, Australian Team Physiotherapist Alex Kountouris said: "Michael Clarke has a longstanding low back injury that requires ongoing management.
"During the recent England ODI series his injury flared up again and has been slow to improve with his regular treatment regime.
"Michael will therefore not be available to play the upcoming India ODI series and will require a more extensive rehabilitation period before returning to competitive cricket," Kountouris said.
Australian T20 squad to play India
George Bailey (captain), Nathan Coulter-Nile, Xavier Doherty, James Faulkner, Aaron Finch, Brad Haddin, Moises Henriques, Mitchell Johnson, Nic Maddinson, Glenn Maxwell, Clint McKay, Adam Voges, Shane Watson
Australian ODI squad to play India
George Bailey (captain), Nathan Coulter-Nile, Xavier Doherty, James Faulkner, Callum Ferguson, Aaron Finch, Brad Haddin, Moises Henriques, Phil Hughes, Mitchell Johnson, Glenn Maxwell, Clint McKay, Adam Voges, Shane Watson.
Schedule (All matches Day/Night)
October 10: T20I: Rajkot
October 13: 1st ODI: Pune
October 16: 2nd ODI: Jaipur
October 19: 3rd ODI: Mohali
October 23: 4th ODI: Ranchi
October 26: 5th ODI: Cuttack
October 30: 6th ODI: Nagpur
November 2: 7th ODI: Bangalore