Heinrich Kühn was the grandson of German sculptor Christian Gottlob Kühn and was related to the German romantic painter, Caspar David Friedrich. Kühn studied music and painting for several months before he served in the military. From 1885 to 1888 he studied natural science and medicine, and experimented with microscopic photography. In 1889 or 1890 he settled in Innsbruck and devoted himself to photography.
Kühn joined the Vienna Kamera-Club in 1894, the same year his works were noticed by Alfred Stieglitz. He won a medal for artistic photography from the club in 1896, and that year his prints were accepted for exhibition at the London salon of The Linked Ring. He began to correspond with Stieglitz, whom he met in Austria in 1904, and who included his work in an exhibition of Viennese and German photography at his Little Galleries of the Photo-Secession in 1906. The following year Kühn met Frank Eugene, Edward Steichen, and Stieglitz in Munich, where they experimented with the new Lumière Autochrome plates. During the same year Kühn began to experiment with the photogravure process, and by 1911 he was proficient enough with the process to present three methods in a Camera Work issue devoted to his work.
Over the next 30 years Kühn continued to experiment with processes and write technical articles for journals. His work was occasionally published in Das Deutsche Lichtbild and was included in historical sections of German and Austrian exhibitions.