The activists climbed the rig in the Pechora Sea, anchoring themselves with mooring lines, after arriving in three inflatable boats around 4 a.m. local time, the environmental organization said Friday.
Members of the group, led by Greenpeace chief Kumi Naidoo of South Africa, include two activists from Germany, and one each from Canada, the United States and Finland.
The Canadian is Terry Christenson from Parry Sound, Ont., who has been an activist with the group for four years.
Greenpeace said the activists did not face much resistance from oil workers and managed to put a banner on the rig, which says: "Don't kill the Arctic."
The platform is about 1,000 kilometres from the nearest port — Murmansk, a city on the extreme northwestern edge of the Russian mainland.
Platform owned and operated by Gazprom subsidiary
Prirazlomnaya is owned and operated by a subsidiary of Russian energy giant Gazprom, which is pioneering Russia's oil drilling in the Arctic. The state-owned company installed the drilling platform there last year and is preparing to drill the first well.
Naidoo said the activists were suspended on portable ledges. They could be seen huddled inside small tents. Greenpeace said they had supplies to last for several days.
Naidoo said many of the platform's employees "have been very friendly, engaging in conversations with us, asking where we come from and offering us soup."
However, he said platform employees also warned them a Russian coast guard helicopter was on its way to detain them.
Gazprom told the AP in an emailed statement the activists "have been invited to scale up to the platform for a constructive dialogue," but said that they refused. The company said that "all work on the platform proceeds as normal."
"The authorities have held their attempts to remove us, but they are harrassing the team by hosing icy cold water," Naidoo said on his Twitter feed. "It looks like they will drive us down pretty soon," he told the U.S. TV program Democracy Now.
"We simply want to make the point that drilling in the Arctic is completely reckless," Naidoo said.
Russian and international environmentalists have warned that drilling in the Russian Arctic could have disastrous consequences because of a lack of technology and infrastructure to deal with a possible spill in a remote region with massive icebergs and heavy storms.
An AP investigation last year found that at least 1 per cent of Russia's annual oil production, or 5 million tons, is spilled every year.
A report by Greenpeace and World Wildlife Fund, issued last week, said that a spill from Prirazlomnaya could contaminate protected areas and nature reserves on the shore and islands within 20 hours, while emergency teams would take at least three days to reach the area.