All-rounder Malinda Pushpakumara, 29, was brought into the squad after he led Sri Lanka A to a three-wicket victory over England Lions in an unofficial Test on Monday, the Sri Lankan board said.
Fast bowler Vikum Sanjaya Bandara, 25, was called up for a second time. He was first named into the Test squad in December for the South African tour, but did not play.
Sri Lanka's regular skipper Angelo Mathews has been left out of the two Tests against Bangladesh, but the Sri Lankan board has not ruled him out of the three One-day Internationals and the two Twenty20 games.
The first Test starts in Galle on March 7. Mathews returned home in January, halfway through the South African tour, after twisting his ankle. Herath filled in for Mathews during Sri Lanka's tour of Zimbabwe in November, when he led his side to victory in both Tests.
Sri Lanka squad: Rangana Herath (capt), Dimuth Karunaratne, Niroshan Dickwella, Upul Tharanga, Dhananjaya de Silva, Kusal Mendis, Asela Gunaratne, Dinesh Chandimal, Suranga Lakmal, Lahiru Kumara, Nuwan Pradeep, Vikum Sanjaya Bandara, Dilruwan Perera, Lakshan Sandakan, Malinda Pushpakumara.