Born in Heusweiler, Fritz Grewenig began an apprenticeship as a painter in the business run by his father. Grewenig attended the School of Decorative Painting in Saarbrücken from 1909 to 1911. He then took lessons from the Saarbrücken painter Richard Wenzel before enrolling at the Dresden Academy of Fine Arts in 1913, where he studied under Richard Müller, Robert Sterl. In 1922, Grewenig set up a private art school in his Saarbrücken studio, and joined the Artists’ Association of the Saarland.
In 1924, Grewenig founded the State Academy of Arts and Crafts in Saarbrücken, of which he remained the director until 1936. After the Saarland was “reincorporated” into greater Germany, the State Academy of Arts and Crafts in Saarbrücken was closed in 1936 and the State Museum was closed down. Grewenig was removed from his post as director by Gauleiter Josef Bürckel. In 1942, Grewenig was banned from exhibiting.