The department of public safety said in a note sent to prefects and police chiefs that "vigilance and control will be intensified" at places of Jewish worship and locations linked to Israel, Ansa reported.
Nathan Graff was attacked while walking alone on via San Gimignano, in a Jewish area of the city, Corriere reported.
A witness attempted to intervene but the attacker, whose face was partially covered, managed to escape, sparking a massive police hunt. There are suspicions that the assailant could have been an Arab woman.
Graff, who lived in Milan and held Israeli citizenship, was stabbed “between three and nine times” outside Carmel Pizza, a kosher pizzeria, and close to a Jewish school.
He was taken to the city's Niguarda hospital, where he underwent surgery for wounds to the face, back, throat and arm. He is in a stable condition.
Renzo Gattegna, the president of the Union of Italian Jewish Communities, said on Friday that Italian Jews would not be intimidated by the attack.
Meanwhile Abdel Hamid Shaari, president of the Islamic Cultural Centre, also condemned the attack, "without ifs or buts of what happened".
Soon after the attack, police were called to a Jewish restaurant on via Sardinia because of a bomb scare, which turned out to be a false alarm.