"Our soldier was killed by rifle fire in the early stages of that conflict," Mr Jones said.
The New Zealand contingent "seemed to hit on a group that was willing to fight back", said Defence Force Chief Lieutenant General Rhys Jones.
Mr Jones said the operation had been going since 9am NZ time and was still being carried out.
He said the shot soldier had been treated by a top military neurosurgeon, but had died on the operating table.
He said Victoria Cross-winning SAS soldier Willie Apiata was not the soldier killed.
A young child and a "fighting age man" has also been injured in the conflict.
Prime Minister John Key said he regretted the loss of another soldier but did not regret the decision to commit to troops to Afghanistan.
Mr Key said the death was a reminder of the volatile and dangerous conditions SAS forces were facing amid rising conflict in Afghanistan.
"This soldier has paid the highest price for his service to this country, and we mourn his loss with heavy hearts," Mr Key said.
"My heart goes out to the family and those who are serving New Zealand but we are doing the right thing."
The Prime Minister, Defence Minister Wayne Mapp and Lieutenant General Jones all expressed condolences to the family.
New Zealand forces will remain in Afghanistan until 2014, while SAS troops will continue their operations until next March. Today's incident did not change those plans, Mr Key said.
He said the SAS were playing a vital role in combating global terrorism.
About 70 members of the 1st Battalion Royal New Zealand Infantry regiment and support units returned from deployment in Bamyan on Monday.
SAS soldier Corporal Doug Grant, 41, was shot dead last month during an operation to rescue hostages at the British Council cultural centre in Kabul, which was being attacked by the Taleban.
Corporate Grant was the first SAS fatality in Afghanistan in four deployments since 2001.
