Beloch was the daughter of the German historian Karl Julius Beloch, who taught ancient history for 50 years at Sapienza University of Rome, and American Bella Bailey.
Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo. She received her degree in 1908 with Lauude and "dignita' di stampa" which means that her work was worthy of publication and in fact her thesis "Sulle trasformazioni birazionali dello spazio" (On Birational Transformations In Space) was published in the Annali di Matematica Pura ed Applicata.
Guido Castelnuovo was very impressed with her talent and offer her the position of assistant which Margherita took and held until 1919, when she moved to Pavia and the successive year to Palermo to work under Michele De Franchis, an important figure of the Italian school of algebraic geometry at the time.
In 1924, Beloch completed her "libera docenza" (a degree that at that time had to be obtained before one could become a professor) and three years later she became a full professor at the University of Ferrara
where she taught until her retirement (1955).