The bodies of Carla Gaveglio, 48, Maria Grazia Ascoli, 77, Gianna Muset, 68, Angelo D'Agostino, 71, and 90-year-old Mario Casati were formally identified by French authorities, the ministry said in a statement.
Their families have been informed.
Nicolas Leslie, an Italian-American student who was born in Italy but grew up in the US, also died, according to reports later on Tuesday. Leslie, 20, was in Nice as part of a university exchange programme.
“[Foreign Minister] Paolo Gentiloni and the ministry express our sympathy and solidarity to the families and friends of the victims of this barbaric attack,” the ministry said in the statement.
A man identified as 31-year-old Tunisian-born Mohamed Lahouaiej Bouhlel drove a refrigerated truck into crowds enjoying a Bastille Day fireworks display on the city's waterfront, the Promenade des Anglais, killing 84 and injuring 202.
Meanwhile, checks were carried out in Italy on Monday on a suspected accomplice, resident in Puglia, of Bouhlel, who was shot dead after the attack.