The ministry spokesman said next of kin had been informed, and media were asked to respect their privacy.
The man, who The Australian said went by the name Muslim bin John and fought under the alias Abu Suhaib al-Australi, was killed alongside another Australian citizen named as Christopher Harvard of Townsville.
They were reportedly killed in a US Predator drone strike on five al-Qaeda militants travelling in a convoy of cars in Yemen, The Australian said.
The incident happened on November 19 but their identities had only just come to light.
Prime Minister John Key said he had been advised that the New Zealander was in Yemen last year and had attended a terrorist training camp.
He was told that it was likely the man had been killed late in 2013, but it took some time to confirm this through DNA testing.
Mr Key was informed about the killing by New Zealand intelligence agencies but said he did not know where they got the information from.
The man was the subject of a New Zealand intelligence warrant.
The Prime Minister would not confirm the man's identity, but said it was not Mark Taylor, a New Zealander with links to al Qaeda.
He confirmed that the man was born in New Zealand and that his next of kin still lived here.
Mr Key said drone strikes were legitimate when countries were trying to contend with very dangerous situations and terrorists without putting their own people in harm's way.
Asked whether the strike which killed the New Zealander was legitimate, he said: "I suspect so, given that three of the people killed were well known al Qaeda operatives."
Green Party co-leader Russel Norman said extra-judicial assassinations were never warranted and eroded respect for the US Government.
"It shows that the United States thinks that it has free reign to assassinate people it doesn't like.
"I think [Barack] Obama is fundamentally wrong in his pursuit of extra-judicial assassinations via the drones."
He questioned whether the GCSB had a role in providing information which assisted with the killing.
Dr Norman said he believed that a New Zealander working for al Qaeda posed a threat to this country. "But if we're going to deal with terrorism, we can't act like terrorists."
Last year Mr Key said during debate of the controversial amendment to the GCSB legislation that New Zealanders with links to al-Qaeda were known to be training in Yemen.
