Residents and tourists will have to get around via bike, electric scooter or public transport from 10:00 (9:00 GMT) to 18:00.
Some streets will remain open to traffic, in particular to allow access to the San Sir Stadium, where AC Milan meets Hellas Verona in the afternoon.
The car ban – which is not the first time that Italy's economic capital has prohibited from driving within city limits – has been met with scepticism by some, with the regional counsellor for the environment, Raffaele Cattaneo, calling it “demagogy with a green sauce”.
- These are the 55 most polluted towns in Italy
- Rome to ban diesel cars from 2024
- 'We breathe in poison': Why the Po Valley is one of the most polluted places in Italy
Milan's mayor, Beppe Sala, himself acknowledged the measure would not solve the city's pollution problem in the long-term, pointing a finger at polluting heating systems and cars.
Smog has been a recurring problem in Italy's industrial north, especially in Milan and neighbouring Turin, and previous authorities have often turned to banning cars.
Earlier this month Milan and Rome enforced bans on the most polluting vehicles amid a “smog emergency” in Italy's biggest cities.
A European Court of Auditors report published in September 2018 found that cars were a “major source of urban air pollution” in Milan and said the most effective measure would be to limit their use.
Earlier this month, Sala proposed that smoking be banned at bus and tram stops, part of a wider plan to ban smoking outright in open spaces by 2030.
The plan will be submitted to the city council in March.