The prime minister of Denmark is the head of government in the Kingdom of Denmark comprising the three constituent countries: Denmark, Greenland and the Faroe Islands. Before the creation of the modern office, the kingdom did not initially have a head of government separate from its head of state, namely the monarch, in whom the executive authority was vested. The Constitution of 1849 established a constitutional monarchy by limiting the powers of the monarch and creating the office of premierminister. The inaugural holder of the office was Adam Wilhelm Moltke.

The monarchy of Denmark is a constitutional institution and a historic office of the Kingdom of Denmark. The Kingdom includes Denmark proper and the autonomous territories of the Faroe Islands and Greenland. The Kingdom of Denmark was already consolidated in the 8th century, whose rulers are consistently referred to in Frankish sources as "kings". Under the rule of King Gudfred in 804 the Kingdom may have included all the major provinces of medieval Denmark.