The ship became stuck in shallow waters outside of the port of Helsingborg.
"The vessel was able to free itself and go into the harbour again and when the police got there, the captain was found to be drunk," said Mattias Hansson at the Swedish coastguard to the TT news agency.
No one was reported to have been injured in the incident. The 90 metre vessel which is sailing under the Maltese flag remains in Helsingborg.
The Local has reported a spate of similar incidents in recent months.
Both the captain and first officer of a cargo vessel which ran aground off Sweden's south-east coast in November 2013 were found to have been drunk at the helm.
The pair were detained, taken on land and handed over to Blekinge police.
The ship ran aground outside of Solvesborg in southern Sweden shortly after 4am on November 25th. The vessel was registered in the Dutch Antilles.
Just one day prior to the incident a cargo vessel ran aground off Landskona on the south-west coast of Sweden.
The captain of the vessel was also arrested after he was found to be under the influence of alcohol.
The Öresund straight stretches from the Kattegatt at the northern tip of the Danish peninsula of Sjælland south past Copenhagen and Malmö. The sound is a mere 4 kilometres wide at its narrowest point.
The Öresund's perhaps most defining feature is the tunnel/bridge link which spans from Sweden just south of Malmö to the Danish capital of Copenhagen.