The announcer says North Korea's leader Kim Jong Un ordered the test.
"North Korea has again demonstrated its complete disregard for its obligations under United Nations Security Council resolutions and for international norms against nuclear testing," Brownlee said.
"Today's test is a highly dangerous affront to the entire international community."
The announcement comes after the US Geological Survey said it had recorded a 6.3 magnitude earthquake exactly at noon Sunday local time, near North Korea's known nuclear test site in Punggye-ri, in the county's northeast region.
The quake was felt in northern China, with emergency sirens blaring in Yanji, near the North Korean border, according to local media.
"North Korea has a choice. It can continue on this path, inviting further pressure and isolation and entrenching poverty and misery for its own people," Brownlee said.
"Or it can choose membership of the international community and the security and prosperity that comes with it. Only North Korea can make this decision."
He said New Zealand will join the international community in considering a response.
Today the state-run Korean Central News Agency released photos of Kim Jong Un inspecting what his government described as a hydrogen bomb that could be attached to a missile capable of reaching the mainland United States.