Thushara has been declared unfit for around four weeks and would be sent home to undergo treatment.
"Thilan Thushara, will return back to Sri Lanka due to a shoulder injury, and as such he will not be match fit for approximately two to four weeks," Sri Lankan Cricket said in a statement on Tuesday.
"Thilan will be sent back and Dilhara Fernando will replace him," it added.
Fernando was due to come to India with the ODI squad but will have to now keep himself mentally and physically prepared for the Tests.
Thushara got injured after banging into Kaushal Silva during training on Sunday and the injury did not heal in time, which forced Thushara to miss the first Test. He was replaced by Chanaka Welegedara only minutes before the match.
Sri Lanka is currently playing the first Test of the three-match series at the Sardar Patel Stadium in Ahmedabad. Thushara was not included in the playing XI for the ongoing match.