With the first match due to take place on Sunday, 11 January, Pant picked up the injury in training ahead of the game and was immediately withdrawn from the squad.
Dhruv Jurel was called up as his replacement despite the 24-year-old being uncapped at the ODI level, although he has played nine Tests and four T20Is for India.
"Pant felt a sudden onset of discomfort in his right lateral abdominal area while batting in the nets during India's practice session on Saturday afternoon at the BCA Stadium, Vadodara," The BCCI said in a statement.
"He was taken for MRI scans immediately and the BCCI medical team had a detailed discussion with an expert on his clinical and radiological findings. Pant has been diagnosed with a side strain (oblique muscle tear) and is subsequently ruled out of the ODI series."
Pant was not expected to be in the starting XI against New Zealand, with KL Rahul ahead of him in the pecking order, so Jurel's call-up is to maintain depth in the squad.
Jurel's call-up is reward for his fine form in List-A cricket so far this season, with six scores of 50 or more in his last seven matches for Uttar Pradesh in the Vijay Hazare Trophy.
After Sunday's game, the three-match ODI series goes to Rajkot on 14 January before concluding in Indore on 18 January. It will be followed by a five-match T20I series beginning in Nagpur on 21 January.