Greenpeace says that the vessel was carrying the first oil from a new offshore platform in the Arctic.
Among those arrested was the captain of Greenpeace’s Rainbow Warrior ship.
Peter Willcox was among campaigners detained by Russia last year after protesting against Arctic drilling.
Thirty people were held on hooliganism charges in September after Russian authorities boarded their ship, the Arctic Sunrise, during an anti-drilling demonstration against the offshore oil rig owned by the Russian company Gazprom.
All 30 were later released in December under a new Russian amnesty law.
‘No Arctic oil’
Greenpeace said rubber rafts launched from the Rainbow Warrior on Thursday successfully blocked the passage of the Russian ship. But Dutch police said it was still able to moor in Rotterdam harbour.
About 80 activists who sailed out in dinghies were involved in the effort to prevent the Russian vessel from reaching the quayside.
The protesters painted “no Arctic oil” in large letters on the hull of the tanker.
Police told the AFP news agency that several activists also climbed a fence to try to prevent the ship from docking.
The oil comes from the Prirazlomnaya oil rig, owned by Gazprom and the site of Greenpeace’s protest last September.
The Gazprom project is Russia’s first effort to extract oil from the Barents Sea. Greenpeace says that it is an environmental catastrophe waiting to happen.
Russia’s economy and its recent growth depends to a large extent on income from its huge oil and gas deposits.