Asalanka replaces Wanindu Hasaranga, who stepped down as skipper in the shortest format after Sri Lanka failed to make the Super Eight stage of the T20 World Cup in the U.S. and West Indies last month.
Sri Lanka and India will play three T20s in Pallekele from Saturday before meeting in three one-day internationals.
Kusal Mendis leads Sri Lanka's ODI side while Dhananjaya de Silva is the Test captain. De Silva and veteran Angelo Mathews were not included in the 16-man T20 squad but there was a place for Hasaranga.
India will also have a new captain in Suryakumar Yadav, who took charge of the T20 team after the retirement of Rohit Sharma following their triumphant World Cup campaign.
T20I squad: Charith Asalanka (captain), Pathum Nissanka, Kusal Perera, Avishka Fernando, Kusal Mendis, Dinesh Chandimal, Kamindu Mendis, Dasun Shanaka, Wanindu Hasaranga, Dunith Wellalage, Maheesh Theekshana, Chamindu Wickramasinghe, Matheesha Pathirana, Nuwan Thushara, Dushmantha Chameera, Binura Fernando.
