"The Ocean Explorer was pulled free," the Danish navy's Joint Arctic Command in Greenland said.
A Greenlandic fisheries research vessel was able to help tug the ship free, said the ship's owner, SunStone.
"There have not been any injuries to any person onboard, no pollution of the environment and no breach of the hull," SunStone said.
The ship, carrying 206 passengers and crew, ran aground on Monday afternoon in the Alpefjord, in the Northeast Greenland National Park.
The Joint Arctic Command said on Wednesday the ship had run aground on sand and mud, not rocks, and tried unsuccessfully to refloat during several high tides.
According to Australian media reports, three people on board have tested positive for Covid.
Most of the tourists were from Australia, Britain, New Zealand, South Korea and the United States.
The cause of the accident was not immediately known.
There are few hydrological surveys of the area where the cruise ship ran aground, making it difficult to assess the sea depths.
Danish police have opened a preliminary investigation into the grounding to determine if there was any wrongdoing.
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