Mathews missed the one-day series in South Africa, the tour of Australia and the home series against Bangladesh with a hamstring injury but is back in action for his Delhi franchise in the ongoing Indian Premier League.
Malinga, feared for his awkward action and toe-crushing yorkers, also returns after completing his rehabilitation following a knee injury which forced him out of the World Twenty20 in India last year.
The 33-year-old, who quit test cricket in 2011, played the last of his 191 one-dayer internationals in 2015 and returned to international cricket with Twenty20 matches in Australia earlier this year.
Sri Lanka also named two standby players -- Dilruwan Perera and Danushka Gunathilaka.
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"I think I've got the best possible team," Mathews told a news conference.
"Plus we are travelling with 17, which gives us a lot more options... if something happens to someone, it's always better to have a couple of players over there," said the 29-year-old.
"It's another opportunity for us to bring a lot of pride back to Sri Lanka. It's an opportunity for us to bring an ICC trophy back home," added Mathews, who was part of Sri Lanka's triumphant 2014 World Twenty20 team.
Squad: Angelo Mathews (captain), Upul Tharanga, Niroshan Dickwella, Kusal Perera, Kusal Mendis, Chamara Kapugedera, Asela Gunaratne, Dinesh Chandimal, Lasith Malinga, Suranga Lakmal, Nuwan Pradeep, Nuwan Kulasekera, Thisara Perera, Lakshan Sandakan, Seekkuge Prasanna
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
