Teachers at the nursery were left shocked when the child kept performing the salute whenever he wanted to say something or bid farewell, La Repubblica reported.
The greeting, which involves holding the arm out straight with the palm down and fingers touching, was adopted by the Italian fascist regime in the 1920s and later within the Nazi party.
The boy allegedly performed the gesture in front of classmates, teachers and janitors, the newspaper said.
When confronted, his parents reportedly said: “What's wrong, these are our political ideals…we want to give him a strict, but at the same time natural, education.”
His father, aged 30, is also alleged to have proudly displayed a swastika tattooed on his arm during the meeting with teachers.
The salute and other fascist symbols were banned by Italy's post-war constitution, but a significant swathe of the population continues to admire the regime and Mussolini.
Read more: The Italians who worship Mussolini
The school has threatened to expel the child if he doesn't stop.
“The greeting is prohibited by Italian law and is not exactly a gesture suitable for a four-year-old, who attends a kindergarten,” one of the teachers was quoted as saying.