The US-drafted resolution, which said the communist state's action was a "clear threat to international peace and security," allows nations to stop cargo going to and from North Korea to check for weapons of mass destruction or related supplies.
The resolution bars trade with North Korea in dangerous weapons. It also imposes bans on heavy conventional weapons and luxury goods and asks nations to freeze funds connected with North Korea's arms programmes.
Pak Gil Yon, North Korea's UN ambassador, walked out of the council after he spoke. He accused members of "gangster-like" action for adopting the resolution and ignoring the threat from the United States against his country.
Pak said Pyongyang considered any further US pressure a "declaration of war".
North Korea has issued similar statements before, but this time it was before a formal audience.
Enforcement will largely depend on whether those who have traded with North Korea honour the bans, which now also have the support of neighbouring China, the closest ally of North Korea, as well as Russia.
A UN sanctions committee will distribute a list of which weapons and related supplies are banned.
George Bush, the US president, said the resolution showed "the world is united in our opposition to its nuclear weapons plans" and Taro Aso, Japan's foreign minister, said North Korea had to "take concrete measures to resolve the issue".
Wang Guangya, the Chinese UN ambassador, said: "China strongly urges the countries concerned to adopt a prudent and responsible attitude in this regard and refrain from taking any provocative steps that may intensify the tensions."
Most of Pyongyang's trade crosses through China, which fears a flood of refugees if the Pyongyang government collapses.
Kim Dae-jung, the former South Korean president, told Reuters in an e-mail interview: "North Korea is already very familiar with poverty.
"The country can also get support, at least in order to survive, from countries such as China."
Kim, the architect of South Korea's engagement policy with the North, blamed US policy in part for the nuclear crisis, which he said could only end if Washington held direct talks with Pyongyang, which the Bush administration rejects.
The Bush administration has been urged to talk to North Korea by Russia, China and some leading Democrats.
Kim said: "We have to talk not only with friends but also with enemies, if necessary."
John Bolton, the US ambassador to the UN, told the Security Council's 15 members: "Today we are sending a strong and clear message to North Korea and other would-be proliferators that there will be serious repercussions in continuing to pursue weapons of mass destruction."
Next week, the Security Council begins considering sanctions against Iran for its refusal to suspend its nuclear programme.
Iran's foreign ministry said on Saturday that threats of sanctions were "psychological war" and that it was more determined than ever to pursue "the peaceful use of nuclear energy".
Vitaly Churkin, Russia's UN ambassador, told reporters after the vote that deliberations were made more difficult because the United States had imposed unilateral sanctions on both North Korea and Iran.
But Bolton told reporters that he hoped Iran would pay attention to the North Korea resolution because deliberation on Tehran's actions would come next.
He said on Thursday: "I'm sure they're watching in Tehran what we do on this North Korea resolution and I hope they watch closely."