"We are not taking the opposition lightly as you cannot take any chances in international cricket," chairman of selectors Lalith Kaluperuma said on Tuesday.
The selectors named all-rounder Thilan Samaraweera and opener Avishka Gunawardene in the One-day squad to strengthen the batting.
They replace pacemen Nuwan Zoysa and Lasith Malinga, who were members of the squad that took part in a recent home tri-series against the West Indies and India.
Sri Lanka will play three One-dayers and two Tests against Bangladesh. The opening match will be played here on August 31, followed by day-night games on September 2 and 4.
The first Test will begin on September 12 and the second on September 20.
"We are resting Zoysa for both the One-day and Test series, while Malinga will play only in Tests," Kaluperuma said.
Middle-order batsman Shantha Kalavithigoda replaces Zoysa in the Test squad.
Kalavithigoda made his Test debut in New Zealand early this year but missed the home series against the West Indies due to a shoulder injury.
Bangladesh arrive here on Wednesday and will play a warm-up game against a Board President's team on Sunday.
One-day squad: Marvan Atapattu (capt), Sanath Jayasuriya, Upul Tharanga, Kumar Sangakkara, Mahela Jayawardene, Russel Arnold, Tillakaratne Dilshan, Chaminda Vaas, Upul Chandana, Farveez Maharoof, Muttiah Muralitharan, Avishka Gunawardene, Dilhara Fernando, Dilhara Lokuhettige, Thilan Samaraweera.
Test squad: Marvan Atapattu (capt), Sanath Jayasuriya, Kumar Sangakkara, Mahela Jayawardene, Thilan Samaraweera, Tillakaratne Dilshan, Chaminda Vaas, Farveez Maharoof, Rangana Herath, Muttiah Muralitharan, Lasith Malinga, Russel Arnold, Gayan Wijekoon, Dilhara Fernando, Shantha Kalavithigoda.