Both Jayawardene and Malinga are currently playing in the ongoing Champions League Twenty20 in South Africa.
Off-spinner Ajantha Mendis, meanwhile, has been overlooked as he is nursing a side strain that he had suffered during the World Twenty20.
Angelo Mathews has been named the skipper of Twenty20 team following Jayawardene's stepping down as captain after Sri Lanka lost the final of the World T20 championship against West Indies earlier this month.
Fast bowler Nuwan Kulasekara will be Mathews' deputy in the game against the Kiwis.
A selector said that both Jayawardene and vice-captain Malinga have been given the jobs for a period of one year.
However, Jayawardene would return as the captain for the first three of the five One-day Internationals against New Zealand, starting November 1.
The 19-year-old off spinner Tharindu Kaushal, a lad from the rural south in the district of Galle, has been included in the ODI squad. He was a member of Sri Lanka Under-19 team that took part in the Youth World Cup in Australia last August.
Sri Lanka T20 squad: Angelo Mathews (capt) Nuwan Kulasekara (vice-capt) Dilshan Munaweera, Tillakaratne Dilshan, Kumar Sangakkara, Dinesh Chandimal, Jeevan Mendis, Lahiru Thirimanne, Thisara Perera, Shaminda Eranga, Akila Dhananjaya, Sachithra Senanayake and Upul Tharanga.
Sri Lanka squad for the first three ODIs: Mahela Jayawardene (capt), Angelo Mathews (vice-capt), Tillakaratne Dilshan, Kumar Sangakkara, Dinesh Chandimal, Lahiru Thirmanne, Thisara Perera, Jeevan Mendis, Nuwan Kulasekera, Lasith Malinga, Shaminda Eranga, Upul Tharanga, Rangana Herath, Akila Dhananjaya and Tharindu Kaushal.
