Leg-break bowler Jeffrey Vandersay has been added to the touring squad as Herath's replacement.
Sri Lanka, who were handed an innings and 239-run defeat by the hosts in the second Test in Nagpur, trail the three- match series 0-1.
The third game is scheduled to be held in the national capital from December 2 to 6.
It was learnt that left-arm spinner Malinda Pushpakumara was Sri Lanka's first choice to replace Herath but the 30- year-old failed the fitness test.
Herath, who last month became the first left-arm spinner to take 400 Test wickets, has been ineffective on this tour thus far.
In the first Test in Kolkata, Herath bowled only eight overs in seaming conditions, but was required to send down 39 overs in the only innings that India batted in Nagpur, after which he complained of back pain.
Vandersay has played 11 ODIs and seven T20Is for Sri Lanka but is yet to make his Test debut.
Sri Lanka squad for 3rd Test: Dinesh Chandimal(captain), Dimuth Karunaratne, Dhananjaya de Silva, Sadeera Samarawickrama, Angelo Mathews, Lahiru Thirimanne, Suranga Lakmal, Dilruwan Perera, Lahiru Gamage, Lakshan Sandakan, Vishwa Fernando, Dasun Shanaka, Niroshan Dickwella, Roshen Silva, Jeffrey Vandersay.
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