New Zealand Cricket said Williamson used a rapid antigen test after experiencing minor symptoms and he has begun five days of isolation.
Coach Gary Stead confirmed Hamish Rutherford would join the squad as Williamson’s replacement, and Tom Latham will captain the side in Williamson’s absence.
“It’s such a shame for Kane to be forced to withdraw on the eve of such an important match,” Stead said.
“We’re all feeling for him at this time and know how disappointed he will be.
“Hamish was with the Test squad earlier in the tour and has been playing for the Leicestershire Foxes in the Vitality T20 Blast.”
The rest of the touring party have returned negative rapid antigen test results and will continue following the tour health protocols of symptom reporting and subsequent testing if required.
Williamson’s side are fighting to keep the series alive in Nottingham this week and his absence is a blow to their hopes of levelling the scores.
England triumphed over New Zealand in the first Test at Lord’s with a match-winning century from former captain Joe Root.