The pair have been taken on land and have been handed over to Blekinge police.
The ship ran aground outside of Solvesborg in southern Sweden shortly after 4am on Monday. The crew of the Dutch Antilles registered vessel numbered six people of whom four are not suspected of any offence.
The vessel was transporting a cargo of lime from Dunkerque in France to Solvesborg. For some reason the crew made an error in their navigation and headed for the significantly smaller harbour of Torsö, according to a report in the local Blekinge Tidning daily.
The Coast Guard (Kustbevakningen) has confirmed that no one was injured in the incident and that the vessel had not leaked any fuel into the Baltic Sea despite significant damage to its hull.
The ship is reported to be equipped with a double hull which provides greater protection.
"It looks fine at the moment. We have noted that the ship has a double hull so will hold much better and the oil tanks are more protected," Mattias Lindholm said.
The Local reported on Sunday about a similar incident off Sweden's west coast.
The captain of a vessel which ran aground off Helsingborg was arrested on Sunday after he was found to be under the influence of alcohol.
The captain claimed in his defence that had only taken a drink after the ship ran aground. After further tests in hospital this claim was dismissed and the captain was arrested on suspicion of being drunk in charge of the ship.
The 88 metre cargo vessel, which was carrying grain to the UK, ran aground on Saturday morning.