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NZC moved Sunday's fifth and final match to Wellington from Tauranga, having already moved the fourth to the New Zealand capital from Auckland.
Australia spinner Ashton Agar said organisers had made the right call.
"They've made sure that they've looked after the players' mental and physical wellbeing and come to the right decision," he told reporters on Monday.
New Zealand's biggest city Auckland went into a seven-day lockdown from Sunday after the emergence of a new local case of the coronavirus of unknown origin.
New Zealand lead the T20 series 2-0 after winning the opening matches in Christchurch and Dunedin.
The third match is on Wednesday.
Several Auckland-based players in the New Zealand squad are awaiting Covid-19 test results before being cleared to play, New Zealand media reported.
With Australia needing to win the last three matches to claim the series, Agar said the lack of fans in Wellington could play into the visitors' hands.
"A home ground advantage always helps when you’ve got a crowd that’s right behind their home team and that’s how it’s been so far," he said.
"It's always a fun crowd here in New Zealand, it’s always a great atmosphere, so for them to not have that particularly on a game that the series hinges on could be a massive advantage for us."