The 30-year-old, who has taken 558 first-class wickets at an average of 19.85, is the only new face in the team, which also saw the return of batting all-rounder Dhananjaya de Silva and seamer Nuwan Pradeep.
Pushpakumara will replace left-arm spinner Lakshan Sandakan, while de Silva, who was out of the squad for the one-off Test against Zimbabwe, has taken place of regular captain Dinesh Chandimal, who has been hospitalised due to pneumonia.
Pradeep, who was sidelined for two weeks due to hamstring niggle, has replaced Dushmantha Chameera in the squad, to be led by Rangana Herath.
Colombo hosts the second Test from August 3 while the third and final match is scheduled at Pallekele from August 12.
Sri Lanka Squad for first Test: Rangana Herath (C), Upul Tharanga, Dimuth Karunaratne, Kusal Mendis, Angelo Mathews, Asela Gunaratne, Niroshan Dickwella, Dhananjaya de Silva, Danushka Gunathilaka, Dilruwan Perera, Suranga Lakmal, Lahiru Kumara, Vishwa Fernando, Malinda Pushpakumara, Nuwan Pradeep.
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