However, seamer Nuwan Kulasekara, who was left out for the recent series against England, has been recalled.
Sri Lanka have named a 16-man squad for the seven-match series, which starts in Christchurch on 11 January.
But Perera has paid the price for a poor run of form, having managed just one half-century in his last 17 innings.
Dimuth Karunaratne played his last one-day game for Sri Lanka a year ago but may now be set to open the batting with Tillakaratne Dilshan.
Karunaratne made 152 in the eight-wicket first Test defeat to New Zealand which has just concluded and was part of the squad for the final two one-day internationals against England, although he did not play in either match.
Lasith Malinga is also included in the squad, subject to the fast bowler passing a fitness test.
Sri Lanka: Angelo Mathews (captain), Tillakaratne Dilshan, Kumar Sangakkara, Mahela Jayawardene, Lahiru Thirimanne, Dinesh Chandimal, Dimuth Karunaratne, Jeevan Mendis, Thisara Perera, Suranga Lakmal, Lasith Malinga, Dhammika Prasad, Nuwan Kulasekara, Rangana Herath, Sachithra Senanayake, Shaminda Eranga.