New Zealand captain Kane Williamson missed the second Test against England which started on Friday, after testing positive for COVID-19 the night before the match.
Tom Latham is captaincing the side in Williamson's absence.
Williamson undertook a Rapid Antigen Test (RAT) after experiencing minor symptoms on Thursday and has now begun his five days of isolation.
Coach Gary Stead on Thursday confirmed Hamish Rutherford will join the squad as Williamson's replacement. "It's such a shame for Kane to be forced to withdraw on the eve of such an important match," Stead said.
"We are 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," he added.