Romano Floriani Mussolini, 18, was part of coach Maurizio Sarri's 23-man group of players for the trip to Verona. The defender did not enter the match, which saw Giovanni Simeone score four times to give Verona a 4-1 win.
Floriani Mussolini, who signed his first professional contract with the club in March, previously said that he hopes he will be judged by his sporting merit, rather than his name.
He is the third child of Alessandra Mussolini and husband Mauro Floriani, and great grandson of Benito Mussolini, who was prime minister of Italy from 1922 to 1943 after a fascist coup.
Alessandra is a former member of the European Parliament for Forza Italia and another of Benito Mussolini's granddaughters, Rachele, won a second term as a city councillor in Rome this month.
A minority of Lazio fans, known as "ultras," have links to the far right and banners expressing pride in the fascist movement have been flown at the Stadio Olimpico.