The consulted works concur in deriving this surname from the ancient Latin personal name Mutius (also documented as Mucius), pronounced muzio in Late and medieval Latin. It is also considered that the surname may derive, in some cases, from a diminutive of Giacomo, specifically through the form Giacomuzzo.

E. Rossoni notes that all the variants of the surname — including the diminutive forms — descend directly from that Latin origin, and adds that for the variant Muzzi a derivation by syncope of dialect diminutive forms of names such as Giacomo, Guglielmo, or Cosimo is also possible. F. De Laurentiis, for his part, indicates that the surname may represent in some cases the aphetic hypocoristic Muzzo, derived from Giacomuzzo, a popular form of Giacomo.

According to Rossoni, the transformation into a surname is documented in the 16th century, with the criminal notary Orlando Muzi of Bibbiena and with the painter Muzi of Raiano. As for geographical distribution, Muzi is typical of the central strip covering the Marche, Umbria, Lazio, and the area of L'Aquila. Muzio shows an important concentration in the west of Lombardy, in the east of Liguria, and in Piedmont, with a presence also in the area of Naples and in Molise. Muzzi extends from the area of Bologna to Rome, passing through Florence, Siena, Umbria, and Lazio, with presences also in the areas of Genoa and Catanzaro.