Gambhir's absence means Murali Vijay will again open the innings with Virender Sehwag, in a must-win match for the Indians at the P Sara Oval.
Sri Lanka lead the series 1-0 after winning the first match, while the second ended in a high-scoring dull draw.
Vijay gave a good account of himself in the second Test, when he scored a half-century in the first innings.
Off-spinner Harbhajan Singh, who missed Sunday's practice session, also seems a doubtful starter.
However, the team management insisted that the off-spinner's injury is not serious and he is only suffering from a minor side strain.
Both Gambhir and Harbhajan have also been rested for the forthcoming tri-series in Sri Lanka also featuring New Zealand.
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