The 31-year-old sustained the niggle in Zimbabwe during India's recent limited over series there and did not bat in either innings of India's only warm-up match ahead of the Galle test starting on Wednesday.
"Murali Vijay will not be fit for the first test. He has not fully recovered and we don't want to take a chance, especially with weather like this, slippery outfield and things like that," Shastri told reporters.
In his absence, Shikhar Dhawan is set to open the innings with the 23-year-old Lokesh Rahul who has played only two tests.
"It's a big blow," Shastri said of the injury to Vijay, who averages 41.75 after 32 tests and is one of India's most consistent batsmen in recent times.
"He is the in-form player, had a fabulous run in test cricket. He has the ability to play the long innings as he has shown. He will be missed."
Shastri was coy about the chances of Cheteshwar Puajra, once considered an automatic selection at number three before a slump in form set in.
"We will have to play the best five batsmen, if he fits into that five, he plays, if he doesn't, he doesn't play," the former India test player said.
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
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