“Ishant Sharma is recovering from chikungunya and will not be available for the first Test match,” Coach Anil Kumble told reporters in Kanpur, where the opening Test starts on Thursday.
Kumble said a replacement has not been sought for Sharma in the 15-member squad that includes three other fast bowlers -- Bhuvneshwar Kumar, Mohammed Shami and Umesh Yadav.
Kohli's India eye New Zealand scalp in 500th Test
28-year-old Sharma has taken 209 wickets from 72 Tests, with seven five-wicket hauls.
Some 14,600 cases of the illness that causes high fever and joint pain have been recorded across the country so far this year.
India announce squad for New Zealand Test series
The numbers are not higher than in previous years, but hospitals in New Delhi have been struggling to cope, sparking a political row over who is to blame for failing to properly prepare for the outbreak.
The Aedes aegypti mosquito, which can carry the Zika, dengue and chikungunya viruses, is prevalent in India, and is most active during the monsoon season from June to September.
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