North Korea confirmed it completed the test on Tuesday, saying it had used a miniature nuclear device in a "safe and perfect manner".
The North had been threatening to undertake the test for weeks, in response to sanctions imposed after its successful rocket launch in December last year.
UN chief Ban Ki-Moon led the global condemnation of the test, with his office saying it is a "clear and grave violation" of Security Council resolutions.
At an emergency meeting in New York, each of the 15 members of the council called the test regrettable.
Council president, South Korea's Kim Sung-Hwan, said there is a clear threat to international peace and security.
US president Barack Obama called the blast "provocative", while North Korea's sole major ally China also denounced the move.
Prime Minister Julia Gillard joined the chorus of disapproval, saying Australia would work for the strongest possible response to North Korea's continuing defiance of the will of the international community.
Speaking from Vanuatu, Foreign Minister Bob Carr said the test will rattle nerves and undermine peace in the north Asia region.
"We see it as deeply disturbing. We're going to work with our colleagues - Japan and South Korea in particular," he said.
"We acknowledge that China has tried very, very hard and sincerely to dissuade North Korea from this deeply destabilising action."
Japan has responded by putting its military on high alert and ordering the air force to take air samples in a bid to detect radiation.
South Korean officials say the North gave the US and China advanced warning of the test.
South Korea's defence minister Kim Kwan Jin has warned that Pyongyang could be preparing for a second nuclear test in the coming days.
"We are on high alert for an additional nuclear test or missile launch so we're fully mobilising combined intelligence resources of South Korea and the United States," he said.
However, the US, who North Korea has been taunting continuously over past weeks, has called for "swift and credible" international action in response.
Last week, North Korea posted a video to YouTube depicting a city similar to New York on fire after an apparent missile attack.
In a written statement, Mr Obama vowed that Washington would remain vigilant and steadfast in its defence commitments to its allies in Asia.
"These provocations do not make North Korea more secure," he said.
"Far from achieving its stated goal of becoming a strong and prosperous nation, North Korea has instead increasingly isolated and impoverished its people through its ill-advised pursuit of weapons of mass destruction and their means of delivery."
Mr Obama complained the test was a "highly provocative act" that, following the North's December 12 ballistic missile launch, undermined regional stability and violated UN Security Council resolutions.
"The danger posed by North Korea's threatening activities warrants further swift and credible action by the international community," he said.
"The United States will also continue to take steps necessary to defend ourselves and our allies."
South Korean analysts say the blast could have yielded an impact of between 6 and 7 kilotons.
The nuclear test is North Korea's third, after earlier tests in 2006 and 2009.
British foreign secretary William Hague said Britain would press for a robust response to the event.
"I strongly condemn this development, which is a violation of UN Security Council Resolutions 1718, 1874 and 2087," Mr Hague said in a statement.
"The UK will begin urgent consultations with Security Council partners calling for a robust response to this latest development."
Meanwhile, Russia said it considered the test a violation of UN Security Council resolutions, according to state media.
"We condemn these actions by North Korea and see them, along with the recent ballistic rocket satellite launch, as a violation of corresponding UN Security Council resolutions," a foreign ministry source told the Interfax agency.
Japan's prime minister Shinzo Abe labelled the test a "grave threat" to his nation that could not be tolerated.
"[The test] is a grave threat to the safety of our country and a serious challenge against the global framework of nuclear disarmament and non-proliferation," Mr Abe said in a statement.
In a statement after its emergency meeting, the Security Council said that because of the "gravity" of North Korea's defiant gesture, the 15-member council "will begin work immediately on appropriate measures".
However, the statement made no direct reference to sanctions.
After the meeting, North Korea insisted it would never give in to "unreasonable" international resolutions against its nuclear arms program.
Jon Yong Ryong, the first secretary of North Korea's mission in Geneva, told the UN Disarmament Forum the prospects of denuclearising the Korean peninsula were deteriorating in the face of US hostility.
"The DPRK will never be bound to any resolutions," he said.
North Korea already faces heavy sanctions.
UN member states can search any North Korean ships carrying suspicious cargo, and there is a ban on selling the North any material and technology that could be used in weapons of mass destruction.