Wicket-keeper Kumar Sangakkara will be vice-captain for the three-week tour which starts on Sunday with the first of three one-day internationals followed by two Tests.
Dammika Prasad, a 22-year-old fast bowler, is the only new face in the Test and one-day squads -- which were picked even before the Sri Lankan team returned from a tour of Australia late Wednesday.
Veteran opener Sanath Jayasuriya has been picked only for the one-dayers, while middle-order batsman Russel Arnold does not find a place in either squad.
Seasoned spinner Muttiah Muralitharan has been selected only for the Test matches.
"The players have been playing non-stop cricket since November and we are concerned about their workload and so decided to rest some seniors," chairman of selectors Lalith Kaluperuma told AFP on Thursday.
"It helps them to take a break and recharge their batteries before two important series against Pakistan and England and also allows us to take a look at some of the young prospects."
Bangladesh are the weakest Test-playing nation.
The first and second one-dayers will be played in Bogra on Sunday and Monday followed by the third in Chittagong on February 24.
The first Test will be in Chittagong from February 27-March 3 and the second in Bogra from March 6-10.
Sri Lanka's Test squad: Mahela Jayawardene (capt), Kumar Sangakkara (vice-capt), Upul Tharanga, Michael van Dort, Tillakaratne Dilshan, Chamara Kapugedera, Prasanna Jayawardene, Muttiah Muralitharan, Malinga Bandara, Farveez Maharoof, Dhammika Prasad, Lasith Malinga, Dilhara Fernando, Thilan Samaraweera, Sajeeewa Weerakoon.
One-day squad: Mahela Jayawardene (capt), Kumar Sangakkara (vice-capt), Upul Tharanga, Sanath Jayasuriya, Jehan Mubarak, Tillakaratne Dilshan, Chamara Kapugedera, Farveez Maharoof, Hasantha Fernando, Dhammika Prasad, Dilhara Fernando, Ruchira Perera, Akalanka Ganegama, Malinga Bandara, Kaushal Lokuarachchi.