Narine, 35, announced his retirement from international cricket in 2023, four years after playing his last match for West Indies against India
The 29-year-old, who last played an ODI for India in 2015, was overlooked by selectors for India's ODI tour of Australia earlier this year, the tour of Zimbabwe in June and the Twenty20 squad for the two matches against West Indies in August.
"The BCCI Medical team has confirmed that Suresh Raina, who is recovering from a bout of viral fever, is ruled out of the first ODI of the Paytm ODI Trophy against New Zealand," Indian cricket board (BCCI) secretary Ajay Shirke said in a statement.
The statement added that there will be no replacement for the left-hander.
Hosts India completed a 3-0 sweep of the Test series against New Zealand earlier this month.