The 32-year-old from Tamil Nadu sustained the injury whilst diving on an outstretched arm during the first Test in Pune, which India lost by 333 runs in less than three days.
"Indian Test opener Murali Vijay has been ruled out of the 2nd Paytm Test between India and Australia in Bengaluru starting March 4th after sustaining an injury to his left shoulder," BCCI said in a release.
Vijay was replaced by Abhinav Mukund, who made a comeback to the Test side after five-and-a-half years.