The news comes a week after the foreign minister told the Danish newspaper Berlingske that only ethnic Inuit people should be allowed to vote in a future vote on independence.
Broberg from Naleraq, a centrist-populist pro-independence political party in Greenland, still remains responsible for business and trade.
Greenland's prime minister said that Broberg's statements were contrary to the government's policy.
The demoted minister, who openly advocates Greenlandic independence, said in a Facebook post that his comments were misunderstood and that all Greenlanders should be allowed to vote in an independence referendum, regardless of their ethnicity.
In 2008, Greenland, an autonomous territory of the Kingdom of Denmark, held a referendum on self-government, in which 75% of the population voted for the possibility of declaring independence at any moment. To do this, they need to gain a majority in a referendum. Greenland's parliament can decide to hold a referendum independently.