Fritz was born as the son of Robert and Minna, née Hünich. His father Robert (1848–1934) was born in Greiz, and his mother Minna (1846–1932) was born in Freiberg. Fritz had five siblings – Mimi, Hans, Hermann, Otto, and Mizi, one of whom, Hans, emigrated to the USA.
Pfleumer began his engineering studies at a university in Dresden in 1897.
Pfleumer had developed a process for putting metal stripes on cigaratte papers, and reasoned that he could similarly coat a magnetic stripe, to be used as an alternative to wire recording. In 1927, after experimenting with various materials, Pfleumer used very thin paper which he coated with iron oxide powder using lacquer as glue. He received a patent in 1928.
On December 1, 1932 Pfleumer granted the right of use to the AEG that based on his invention built the world's first practical tape recorder called Magnetophon K1. It was first demonstrated at the IFA in 1935.