Senior batsman Ross Taylor will lead the tourists in place of an ailing Williamson, whose absence represents a body blow to New Zealand's hopes of levelling the series after their comprehensive defeat in the series opener in Kanpur.
New Zealand made three changes to that side, bringing in Henry Nicholls, Matt Henry and Jeetan Patel for Williamson, off-spinner Mark Craig and leg-spinner Ish Sodhi.
Craig has been ruled out of the remainder of the tour with a side strain he sustained in the first match of the three-test series.
India, playing their 250th home test, made a couple of changes, bringing back opener Shikhar Dhawan for injured Lokesh Rahul, while Bhuvneshwar Kumar replaced fellow paceman Umesh Yadav.
"It's a pretty hard surface with good cover of grass. First overs will be challenging," Kohli said at the toss.
Taylor said he felt New Zealand were competitive in Kanpur and would try to do better in Kolkata.
"Some of our batters got valuable time in the middle and I thought our bowlers put the ball in the right areas for long enough to put this Indian side under pressure," Taylor said.
Teams:
India: Murali Vijay, Shikhar Dhawan, Cheteshwar Pujara, Virat Kohli (captain), Ajinkya Rahane, Rohit Sharma, Ravichandran Ashwin, Wriddhiman Saha, Ravindra Jadeja, Bhuvneshwar Kumar, Mohammed Shami.
New Zealand: Tom Latham, Martin Guptill, Henry Nicholls, Ross Taylor (captain), Luke Ronchi, Mitchell Santner, BJ Watling, Jeetan Patel, Neil Wagner, Matt Henry, Trent Boult.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
