Police told Greenland broadcaster KNR on Monday that investigations of the defacement of the statue of Hans Egede, a Lutheran missionary who arrived on the vast island in 1721, were ongoing.
The suspect was not identified.
The statue in Nuuk’s old district was vandalised early on Sunday as Greenland was marking its National Day.
It has been vandalised before.
Statues and monuments of people associated with racism or colonialism have been targeted in light of the killing of George Floyd in Minneapolis last month.
Mr Egede, who was born in Norway that was part of Denmark at the time, is considered to be the person who colonised Greenland and founded the capital, Nuuk.
Greenland was a Danish colony until 1953 when it became a formal part of the Danish Realm.
In 2009, Greenland became a self-governing entity.