The announcement came after US President Donald Trump said he would "get Greenland", saying the autonomous Danish territory is needed for his country's "international security".
The island and its mineral resources have become a prized target while melting ice in the Arctic has opened up new shipping routes around it.
"We must face the fact that there are serious challenges regarding security and defence in the Arctic and North Atlantic," Denmark's Defence Minister Troels Lund Poulsen said in a statement.
His announcement came ahead of a visit by the country's Prime Minister Mette Frederiksen to Berlin, Paris and Brussels this week to shore up "European unity" on Greenland.
"Europe is facing a serious situation. With war on the continent and shifts in the geopolitical reality. In moments like this, unity is crucial," Frederiksen said in a statement.
She said she would meet with French President Emmanuel Macron and German Chancellor Olaf Scholz as well as with Mark Rutte, secretary general of the NATO transatlantic defence alliance.
"Denmark is a small country with strong allies. And it is part of a strong European community where together we can meet the challenges we face," Frederiksen said.
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