The Blackcaps skipper will begin five days of isolation after returning a positive sample on a rapid antigen test on Thursday (June 9).
New Zealand Cricket confirmed the rest of the touring party returned negative tests.
Blackcaps coach Gary Stead shared obvious disappointment over losing his captain, while confirming Hamish Rutherford will join the squad.
“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.”
Williamson made scores of two and 15 in England’s win in the first Test at Lord’s, with Matthew Potts claiming his wicket in both innings.
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