Air traffic will stop on Friday for two weeks, including domestic routes which are crucial for transport as the vast island has few roads. Only medical flights will be authorised, the head of the local government Kim Kielsen announced late Tuesday.
Primary schools are to close on March 23 for two weeks.
The decision came after health officials announced the island's first case of COVID-19.
Greenland, which had already banned public gatherings of more than 100 people, is a semi-autonomous Danish territory.
It is home to around 57,000 people, most of them from the indigenous Inuit community.
Denmark, which has reported four COVID-19 deaths, has already closed its borders and schools, banned public gatherings of more than 10 people, and ordered most commercial businesses like hair salons, stores and bars to shut