Three of the 42 trees went up in flames in the overnight attack by vandals, though only one suffered extensive damage to its trunk.
The incident followed protests on Saturday organized by the anti-immigrant Northern League party and CasaPound, a radical rightwing movement. Demonstrators waving the Italian flag stood in front of a large banner alleging the "Africanization" of the historic piazza.
The palms, some of them five metres (17 feet) tall, appeared on Thursday in the shadow of the 14th century Gothic cathedral.
Critics complained not only that the plants were non-native, but that the project - which will also involve banana trees - had been sponsored by Starbucks.
The US coffee giant is preparing to take on the Italian market, a frontal assault on the nation's cherished network of mostly independent bars and cafes.
READ MORE: Get ready - up to 300 Starbucks stores are coming to Italy
Palms are not native to Italy but are widespread in more temperate areas of the country, including Rome and the Riviera, as well as in Sicily, where their juxtaposition with the austere architecture of Norman cathedrals is a favourite holiday snap for visitors.
Some palms in Italy are older than the country itself, having been brought to the peninsula by novelty-seeking aristocrats in the 18th and 19th centuries.
They were later championed by fascist dictator Benito Mussolini as symbols of Italy's short-lived African empire.
The ones in Milan are a cold-resistant variety that are expected to survive the northern city's chilly winters.