According to New Zealand Cricket, Mark Chapman, an Auckland batsman, will replace Williamson as the team's captain for Tuesday's third T20 match in Napier.
Williamson's appointment was not related to the long-standing elbow issues that have plagued the Black Caps captain, according to coach Gary Stead, who did not provide any other information.
On Monday, Stead added, "It's something he's been trying to get booked in for a while.
"An chance has now presented itself, and we have chosen to have Kane seize it."
After the first match in Wellington was rained out, India destroyed the hosts by 65 runs in the second T20 on Sunday in Mount Maunganui, taking a 1-0 lead in the three-match series.
Prior to the first ODI of the series at Eden Park on Friday, Williamson will reunite with the team in Auckland on Wednesday.
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