World T20 Schedule
Both Sangakkara and Kulasekara are nursing injuries which they sustained during the last month's five-match One Day International series against India.
"Please note that Kumar Sangakkara and Nuwan Kulasekara have been selected subject to their recovery from the prevailing injuries," Sri Lanka Cricket said on its website while announcing the squad on Thursday.
The team will be captained by Mahela Jayawardene with Angelo Mathews as his deputy.
Spinner Ajantha Mendis has made a comeback into the team.
ICC World T20 will be held in Sri Lanka from September 18 to October 7. Sri Lanka also named their women's squad for the tournament.
Sri Lanka men's squad: Mahela Jayawardena (captain), Angelo Mathews (vice-captain), Kumar Sangakkara, Tillakaratne Dilshan, Lahiru Thirimanne, Jeevan Mendis, Dilshan Munaweera, Thisara Perera, Lasith Malinga, Nuwan Kulasekara, Rangana Herath, Ajantha Mendis, Dinesh Chandimal, Shaminda Eranga, Akila Dhanajaya
Sri Lanka women's squad: Shashikala Siriwardane (captain), Sandamali Dolawatha, Delani Manodara, Chamari Attapatu, Deepika Rasangika, Ishani Lokusuriya, Chamani Seneviratne, Sripali Weerakkody, Udeshika Prabodini, Maduri Samudrika, Inoka Ranaweera, Prasadini Weerakkody, Inoka Galagedara, Nilakshi Silva.