Demonstrators in Copenhagen and Nuuk chanted slogans such as 'Greenland is not for sale' and 'Hands off Greenland', asserting the territory's right to self-determination.
Trump has previously stated Greenland is vital to US security due to its strategic location and mineral wealth, even refusing to rule out military intervention.
The protests highlight a diplomatic rift between the US and Denmark, both NATO members, with European nations dispatching military personnel to Greenland at Denmark's request.
Greenland, home to 57,000 people, remains part of Denmark, with its parliament favouring independence but preferring to stay with Denmark rather than join the US.