Born in Pontremoli, at club youth level, Albertosi represented the Spezia youth academy for a season, before making his debut in Serie A at the age of 18 for Fiorentina on 18 January 1959, playing in a goalless draw with A.S. Roma.
Albertosi was involved with the Italian "Totonero" betting scandal of 1980 and was ultimately suspended for 2 seasons.