The activists, having breached a 1,650-feet (500-meter) security perimeter around the Stena Don rig off western Greenland, climbed up the rig and fastened themselves to it, police spokesman Morten Nielsen told The Associated Press.
The breach triggered an automatic shutdown of the rig's operations.
The activists are still on the rig and will be arrested, said Nielsen.
"When someone breaks the law — and it has happened here — the person or persons will be prosecuted," Nielsen said by telephone from Nuuk, the capital of Greenland.
Greenland is a semiautonomous Danish territory, and police have been monitoring the activists from a Danish navy ship patrolling the area.
The Danish navy, for its part, said it had no immediate plans to remove the activists, saying it was up to Greenland's police to decide what to do.
"Right now we're waiting to see what happens," naval spokesman Michael Hjort told the Greenland newspaper Sermitsiaq. "We are ready with our dinghies in case the activists fall in the water."
Greenland Premier Kuupik Kleist called Greenpeace's stunt an "openly illegal act" and a "gross violation" of safety rules.
"It is really worrying that Greenpeace uses all means to break the safety rules made to protect human lives and the environment in its quest for media coverage," Kleist said in a statement.
Last week the Greenpeace ship Esperanza anchored near the rig as part of a campaign to protest deepwater oil drilling. Scotland-based Cairn Energy PLC announced at the time that it had discovered natural gas in the area but failed to find crude oil. Cairn Energy has not specified the size of possible oil and gas reserves.
The drilling in the Arctic has sparked condemnation from Greenpeace, whose activists are worried that an oil rush would damage the region's fragile ecosystem.
Cairn had no immediate comments to the rig shutdown.
Drilling for fossil fuels off Greenland's west coast resumed in 2001, three decades after a previous effort failed to find oil. Exploration so far has been mostly unsuccessful.