Fritz Schäfer (or Schaefer) studied medicine at several German universities and qualified as a medical practitioner in 1905. A medical dissertation by him, Zwei Fälle von Lymphosarcom des Herzens (20 pp) was published in Greifswald in 1911.
Schäfer moved to German South West Africa (now Namibia) in 1907. For some time he was a medical practitioner on the Lüderitz-Keetmanshoop railway, collecting plants mainly in the Klein Karras area. However, from 1911 he was associated with the Deutsche Diamantgesellschaft and worked in the vicinity of Lüderitz. He collected plants from 1909 to 1913 and sent some of his specimens to the Botanischer Garten und Botanischer Museum in Berlin, Germany. In 1914 he returned to Germany and served in Europe during World War I (1914-1918). After the war he settled in Küstrin, in the state of Brandenburg, and in 1920 went to Spitzbergen. He returned to his birthplace Görlitz in 1927.
Schäfer donated 750 plant specimens to the Senckenberg Museum of Natural History in Görlitz during 1910/11 and 100 more during 1915/6, followed by his whole collection in 1927. Taxa based on his plants were described by various botanists and several species were named after him: Celosia schaeferi (by H. Schinz*), Zygophyllum schaeferi (by H.G.A. Engler*), Ferraria schaeferi (by M.K. Dinter*), Manulea schaeferi, Ammannia schaeferi, Ceraria schaeferi and Lycium schaeferi.