After completing his schooling in Stuttgart, Hetsch began studying mathematics at the Eberhard Karls University of Tübingen. However, after only two semesters, he returned to Stuttgart and began studying architecture under Gottlieb Christian Eberhard von Etzel. When his father Philipp Friedrich moved to Paris in 1808, Hetsch joined him. From 1809, Hetsch studied at the École des Beaux-Arts under Charles Percier and later under Percier's student Louis-Hippolyte Lebas. With the support of his teachers, Hetsch became an assistant to Jean-Baptiste Rondelet. After some preliminary work, Hetsch became Rondelet's site manager for the construction of the Panthéon. Forced by the political situation, Hetsch returned to Germany in 1812 and settled in Stuttgart. There, he successfully passed his master builder's examination in the same year.
As the Wars of Liberation prevented him from practicing his profession, Hetsch undertook a study trip to Rome. There he made the acquaintance of the Danish architect Peder Malling, who introduced him to the landscape painter Johan Fredrik Eckersberg and the sculptor Bertel Thorvaldsen, among others. When Malling returned to Copenhagen in October 1815, Hetsch joined him. In 1816, Hetsch was appointed lecturer at the School of Ornamentation, where he taught aspiring architects. This school was affiliated with and supported by the Academy of Fine Arts. For his lessons, Hetsch began to compile a collection of drawings, which were intended as models for his students. In 1818, this collection was purchased by the Danish court and left to him for further use. Through his work as a lecturer, Hetsch soon became friends with the architect Christian Frederik Hansen.
In 1820, the academy accepted Hetsch as a member, and in 1822 he was granted Danish citizenship. At the age of 34, Hetsch was appointed professor of perspective at the Royal Danish Academy of Fine Arts in Copenhagen in 1822. There he was instrumental in the design and construction of the New Synagogue, several new buildings at the University of Copenhagen, and the construction of what later became the Catholic Cathedral of St. Ansgar. Together with Christian Frederik Hansen, Hetsch redesigned the interiors of Christiansborg Palace. This work brought him to the attention of the court, and in 1828 Hetsch was entrusted with the management of the Royal Porcelain Manufactory. Between 1829 and 1830, Hetsch traveled through Germany, France, and Italy to, in his own words, "...trace the origins of modern architecture." In 1851, he visited the World's Fair in London with a state delegation and four years later the World's Fair in Paris. At the age of almost 76, Gustav Friedrich von Hetsch died in Copenhagen on September 7, 1864. In his memory, the sculptor Edvard Harald Bentzen created a monument in Copenhagen in 1902.