Williamson picked up a bug and was unable to train at Eden Gardens on the eve of the match.
Opening batsman Tom Latham said he took the final day of preparations off to get well for the first day of the test.
"Kane's also a little bit crook today so he won't be training but no discomfort. I think he's just down with a bug, so nothing too major, but he's just resting up and getting right for tomorrow," Latham said.
On the selection front, the Black Caps may go into the game with just two spinners this time in Jeetan Patel and Mitchell Santner, and play Doug Bracewell ahead of Ish Sodhi.
Patel only landed in Kolkata yesterday and has not played a Test since 2013.
But speaking just hours after touching down in Kokata, the 36-year-old said he was raring to go.
"I'm just excited to be here you know, I didn't think I'd ever play Test cricket again. But to come over [and] join a young bunch of lads that are going somewhere is pretty special," Patel said.
"It's another challenge tomorrow against what are a high-quality side so you know, I'm going to have to be on my form tomorrow. It's a shame I only arrived this morning but hey, that's just life."
India currently lead the Three-test series 1-0 after winning the first Test by 197 runs in Kanpur.