Malinga had ankle surgery in September and just returned to action in Sri Lanka's two warm-up matches, against South Africa and Zimbabwe, prior to the World Cup.
The mercurial paceman missed the recent series against the World Cup co-hosts, who went on to comfortably win the seven-match ODI series 4-2 to give themselves a confidence boost ahead of the global showpiece.
"Lasith will definitely play and he is fit to go," Mathews told reporters on Friday, before declining to name his 11 for the opening match.
Malinga has been a key component of Sri Lanka's performances in the last two World Cups, where they have made the final both times, particularly at the death with his late swinging yorkers proving unplayable at times.
His absence was noticed during the recent one day series, where Sri Lanka looked out of sorts during their buildup to the tournament, having arrived in New Zealand in mid-December and lost the test series 2-0 and then the ODI series.
To top that off, they were well beaten by Zimbabwe in their final World Cup warmup match at Lincoln earlier this week.
The team have also been too reliant on the big three of Tillakaratne Dilshan, Kumar Sangakkara and Mahela Jayawardene to score their runs while their pace attack has looked tame without the blonde-tinted hair of Malinga charging in.
"We had a couple of bad practice matches but we are not concerned about it because we were giving guys opportunities," Mathews said of their final warmup clashes.
"We have a fairly experienced team but the past is the past and we can't look too far ahead. We need to take each game as it comes.
"We've got to be aggressive and play good cricket to win against New Zealand. They're on a roll so we need to back our strengths and go out there and be positive."
Malinga's return to the side will provide a definite challenge to Brendon McCullum's side, though the New Zealand captain said they had spoken at length of facing the 31-year-old, particularly at the end of an innings when he is most lethal.
"We have done a lot of preparation for him," McCullum said. "He is a world class bowler and makes a significant impact to their bowling lineup.
"He is a fantastic death bowler and Sri Lanka is certainly a better side with Lasith Malinga in it."
(Editing by Sudipto Ganguly)
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