"We just learned from police that all six activists have been arrested," Greenpeace spokesperson Therese Jacobsson told the TT news agency.
However, police haven't been able to confirm the arrests, but according to a statement from the Blekinge County poilce, all six activists are suspected of unlawful entry.
The arrests come several hours after the activists boarded the Finnish-flagged "Nordica" in Swedish territorial waters near the Baltic island of Öland.
"Six Greenpeace activists from Finland, Israel, Austria, Sweden and Denmark boarded the Nordica south of the Swedish island of Oeland," Greenpeace Nordic spokesman Juha Aromå told AFP, adding that the activists had scaled the ship shortly after 4am.
The Swedish coast later towed the ship to dock in Karlskrona, southern Sweden, where police were able to get better access to the activists.
The Nordica is one of two Finnish state owned ice-breakers which will be investigating the oil potential inside the Arctic Circle this summer in cooperation with Shell. It is the second time this week that activists have tried to stop its progress.
The activists begun their mission early on Thursday when the ship was at sea south of Öland, off Sweden's south-easterly coastline.
“There is no violence, but this must be stopped in some way,” said Klas Hansén, an officer of the Swedish Coast Guard to TT earlier on Thursday.
According to the Coast Guard, three of the six activists had chained themselves to a crane on board the ship, and Greenpeace have indicated that they have no intention of giving themselves up.
“When I spoke with them before they went on board they were firmly intending to stay,” said Dima Litvinov, a spokesman of Greenpeace, to TT.
"Some of them are stuck fast, so there will be no easy way to free them."
The activists aim to delay the ship as much as possible in the hope of preventing the summer's planned oil drilling.
The organization's action is meant to protest Shell's plans to drill for oil in a sensitive marine area off the north coast of Alaska.
Greanpeace is also frustrated that Sweden has failed to use its position as the current chair of the Arctic Council to prevent the drilling.
A video released by Greenpeace showed the activists in colourful padded jumpsuits and helmets speeding up alongside the icebreaker in small rubber boats before scaling the side of the ship and hanging up banners with "Stop Shell" and "You can save the Arctic".
The Nordica, owned by Finland, was due to join its sister ship, the Fennica, to support two drill ships en route to the north coast of Alaska.
There, there are expected to drill five exploratory wells for Shell in the Chukchi and Beaufort Seas respectively, according to Greenpeace.
The Fennica left Helsinki in March.
Environmentalists have pointed to the vastly complicated task of drilling in the harsh Arctic environment, the difficulty of effectively cleaning up any spills in such conditions, and the risks posed to wildlife and native communities in the region's fragile ecosystem.