Williamson will replace Aaron Redmond at number three in the order. The 2nd Test will be played on a Wellington wicket tailor-made for bowlers.
Williamson, who bats at number three, fractured his left thumb playing against Bangladesh in late October. His withdrawal opens the way for Aaron Redmond to return to the side after a five-year absence.
New Zealand selectors said they believed a broken thumb Williamson sustained in Bangladesh in October will be healed enough for him to take the field for the first Test in Dunedin on Tuesday.
New Zealand called up Otago batsman Aaron Redmond to replace the sick Jesse Ryder for the World Twenty20, the Black Caps said on Thursday.
New Zealand announced they'd called up Otago batsman Aaron Redmond as potential cover for the injured Jesse Ryder in case the opener is ruled out of Wt20.