The 29-year-old had been expected to play in Sunday's opening match after being named in the 15-member squad for the first three ODIs against the visitors.
Ashwin leads India's whitewash of New Zealand
There will be no replacement for Raina "who is recovering from a bout of viral fever", the Board of Control for Cricket in India (BCCI) said in a statement.
The left-hander, who last played in October 2015, was overlooked for India's one-day series against Australia at the start of the year and against Zimbabwe in June.
India take charge of Indore Test after Ashwin's heroics
Mahendra Singh Dhoni returns to lead the ODI team in the five-match series after the hosts whitewashed the Black Caps in the three Tests that concluded Tuesday in Indore.
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