Italy enforces sweeping new coronavirus measures
However, shops and most businesses will remain open.
The government has warned that the rise in cases was causing a huge strain on the country’s health services.
However, Prime Minister Giuseppe Conte said that a full lockdown would be catastrophic for the economy.
Italy was among the first European countries to be badly hit by the virus but a national lockdown in March flattened the curve. Since then, the number of daily cases has climbed steadily and Sunday saw a new record of more than 21,200 infections.
Regional governments had asked for all classes to be conducted via distance learning, Italian media reported, but the move was opposed by Education Minister Lucia Azzolina.
The government is also urging people not to travel outside their home towns or cities unless absolutely necessary and to avoid using public transport if possible.