Høegh-Guldberg was of humble background. He earned a theology degree in 1753, and in 1761 became professor of rhetoric at Sorø academy. He was appointed tutor to Prince Frederick, half brother of the future king Charles VII, in 1764. As Frederick's private secretary in 1771, he shared Frederick's hostility to Count Johann Friedrich Struensee (Struensee, Johann Friedrich, Graf von), then supreme in Denmark through his domination of Christian VII; Høegh-Guldberg took part in a conspiracy that led to Struensee's arrest and execution in 1772.

Thereafter, Høegh-Guldberg, along with Prince Frederick and the dowager queen Juliana Maria, gained significant power in the Danish state. In 1774 Høegh-Guldberg was made confidential cabinet secretary. Soon, without consulting the other council ministers, he was issuing orders signed by the incompetent Christian VII. He took over control of foreign policy after dismissing foreign minister Count Andreas Peter Bernstorff in 1780. Høegh-Guldberg was forced out of power during a 1784 coup d'état led by Prince Frederick. Thereafter, he served as a provincial official, returning also to scholarship.