Cricket Australia postponed a three-match series due to take place in August at a neutral venue, saying the situation for women in the Taliban-ruled country was deteriorating.
It was the third time since 2021 that Australia have refused to play Afghanistan outside of international tournaments.
New Zealand said they will play a one-off Test against Afghanistan at a venue yet to be decided.
They also face Afghanistan in their opening T20 World Cup match in the West Indies in June.
New Zealand Cricket said the decision to go ahead had been taken after discussions at board level and with the players' association.
"The consensus view was that a boycott in isolation would change nothing in Afghanistan," said New Zealand Cricket spokesman Richard Boock.
"It would be more constructive to keep dialogue and participation channels open, while continuing to advocate strongly for change."
Cricket has surged in popularity inside Afghanistan in recent years, fuelled by triumphs over bigger nations on the international stage.
But under the Taliban's brand of Islamic rule, women are effectively barred from the game.
Afghanistan also usually play their "home" fixtures at neutral venues, mainly in the UAE.
"NZC strongly believes that cricket is a game for everyone and would like to see far greater support for the women's game in Afghanistan in the short to medium term," Boock said.
