He looks certain to be named in Australia's squad for the World Cup in West Indies and the United States
Former captain Ross Taylor will lead the side at Eden Gardens instead. New Zealand are 1-0 down in the three-match series.
Williamson did not train with the team on Thursday after becoming ill but initial indications were that he might be able to play.
New Zealand Cricket tweeted, however, that Williamson would not be available for the match, which begins at 0930 (0400 GMT).