Public opinion polls in the run-up to the referendum have suggested that a large majority plan to vote in favour of greater autonomy for Greenland, which was granted semi-autonomy from Denmark in 1979.
Polling stations open at 9:00 am (1200 GMT) and close at 8:00 pm (2300 GMT).
The result is expected around midnight (0300 GMT Wednesday).
According to a poll published on the eve of the plebiscite, 61 percent of voters said they would vote "yes" to self-rule and 15 percent said they would vote "no.
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A total of 19 percent said they were undecided and five percent did not plan to vote at all. The poll was published in the online edition of the island's biggest daily Sermitsiaq.
If the "yes" side wins, the local Greenland government has the chance to take control of new areas such as natural resource management, justice and police affairs and to a certain extent foreign affairs.
There are potentially lucrative revenues from the natural resources under Greenland's seabed, which accordi