Usha Vance, wife of Vice President JD Vance, will lead the delegation that includes White House national security adviser Mike Waltz and Energy Secretary Chris Wright.
Waltz and Wright plan to visit the Pituffik space base, the US military base in Greenland. The White House said they will get briefings from US service members there.
They will then join Vance to visit historical sites and attend the national dogsled race.
Brian Hughes, spokesman for the White House National Security Council, said the US team is "confident that this visit presents an opportunity to build on partnerships that respects Greenland's self determination and advances economic co-operation".
"This is a visit to learn about Greenland, its culture, history, and people and to attend a dogsled race the United States is proud to sponsor, plain and simple," Hughes said.
Trump has made US annexation of Greenland a major talking point since taking office in January.
Greenland's strategic location and rich mineral resources could benefit the US It lies along the shortest route from Europe to North America, vital for the US ballistic missile warning system.
The governments of both Greenland and Denmark have voiced opposition to such a move.
The Greenlandic government, which is in a caretaker period after a March 11 general election won by a party that favours a slow approach to independence from Denmark, did not reply to requests for comments.
Danish Prime Minister Mette Frederiksen said in a written comment reacting to news of the visit that "this is something we take seriously".
Denmark wants to co-operate with the US, but it should be co-operation based on "the fundamental rules of sovereignty", she said.
She added that dialogue with the US regarding Greenland would take place in close co-ordination with the Danish government and the future Greenlandic government.Â
