The Liberian-flagged Arctic Sky will now head for Riga, Latvia for repairs.
The Arctic Sky was carrying wood from Finland to Egypt when it ran aground outside of Singö near Norrtälje, north of Stockholm.
"The vessel has passed by the wrong side of the Understen lighthouse and you can't get through there by ship," Kenneth Neijnes, at the Swedish coastguard said.
Neijnes said there had been no oil leak and the ship had not been in danger of sinking, while media reports said it had hit rocks. Divers found it was only slightly damaged.
The Arctic Sea, owned by the Finnish Solchart Management company, was allegedly seized by pirates in the Baltic in July and then recaptured by the Russian navy in August off west Africa.
There remains a cloud of mystery surrounding the Arctic Sea amid speculation has raged that the ship might have been carrying a clandestine cargo.