Atapattu, 36, was part of the squad at this year's World Cup in which Sri Lanka lost to defending champions Australia in the final but he did not feature in any of their matches.
Chief selector Ashantha de Mel told reporters Atapattu had been left out to give opportunities to younger players.
"We felt we could take this opportunity to have a look at some young players," said de Mel.
Three other senior players - Muttiah Muralitharan, Chaminda Vaas and Kumar Sangakkara - are also missing due to
Two uncapped players - fast bowler Ishara Amarasinghe and batsman Malintha Warnapura - are included for the first time.
Wicketkeeper Prasanna Jayawardene replaces Sangakkara.
Sri Lanka leave for Abu Dhabi on May 15 and will play three games starting on May 18.
Squad:
Mahela Jayawardene (Capt), Sanath Jayasuriya, Upul Tharanga, Chamara Silva, T.M. Dilshan, Farveez Maharoof, Dilhara Fernando, Malinga Bandara, Lasith Malinga, Malintha Warnapura, Prasanna Jayawardene (Wk), Ruchira Perera, Ishara Amarasinghe, Kaushal Lokuarachchi, Chamara Kapugedara
