Malinga is still recovering from a knee injury sustained during the West Indies tour of Sri Lanka in October and November.
"He has not come for the ODIs. He's feeling some discomfort in his knee. Whether he will come between the ODIs and T20s -- no-one knows," team manager Jerry Woutersz said.
Thisara Perera has joined the squad in Malinga's place ahead of the first ODI in Christchurch on Saturday. New Zealand also have injury concerns with Kane Williamson, the newly crowned number one Test batsman in the world, suffering discomfort in his right knee.
"We're just working through that knee. It's just a little bit niggly so we want to make sure it's 100 percent," New Zealand batting coach Craig McMillan said.
"If it's not Tom is the man we'll bring in as cover.