Viking Line spokesperson Johanna Boijer-Svahnström on Sunday said Viking Grace was carrying Finnish passengers from Mariehamn back to the mainland, while Swedish passengers would board sister ship Viking Amorella for travel to Stockholm.
Coast guard divers did not detect any leaks in the vessel following inspections on Saturday and Sunday.
Some 300 Viking Grace passengers spent the night on the stranded ship that ran aground on Saturday afternoon off the port of Mariehamn.
Passengers told Yle that the atmosphere on the ship had been calm, though many had hoped to disembark on Saturday.
While officials have yet to determine the cause of the accident, Boijer-Svahnström said storm-force winds played a role in the ship running aground.
As of Monday, Viking Line's Gabriella will replace Viking Grace departures from Turku. Viking Grace operates the company's Stockholm-Åland Islands-Turku route.
Saturday's accident was Viking Line's second incident this autumn. In September passengers evacuated Viking Amorella after it ran aground in the Åland archipelago.