Skipper Kane Williamson has been quarantined from his team-mates after going down with a virus which ruled him out of the second Test against India, New Zealand Cricket said on Friday.

In a blow to the tourists' hopes of levelling the series, Williamson was omitted from the Black Caps team after he also missed training on Thursday.

"Kane Williamson has been ruled out of the Black Caps 2nd Test in Kolkata with illness. Ross Taylor will captain side," the Black Caps tweeted on Friday, just a few hours before play began.

Williamson has a viral illness and is also suffering from fever and dehydration, according to New Zealand's Fairfax media.

New Zealand Cricket told AFP it was "standard practice" to separate somebody who was sick from his team-mates.

Williamson not only provides leadership for New Zealand but he is also their most consistent batsman, scoring 75 in a 124-run second-wicket partnership with Tom Latham in the first Test in Kanpur.

New Zealand need a win at Eden Gardens to square the three-match series at 1-1 after losing the Kanpur Test by 197 runs.