Officers were called to the incident in the Rampant Horse Street store just before 12pm on Saturday, where Animal Rebellion protestors were protesting.
In a Tweet Norwich Police said: “Following reports of a disturbance at M&S, Rampant Horse Street, four people have been arrested for offences of assault and criminal damage.”
Meanwhile, Home Secretary Suella Braverman has announced she plans to crackdown on the kinds of protests favoured by climate activists.
It is understood that police will get new powers to be able to take a more “proactive” approach to some protests, with some of the measures specifically targeted at the tactics used by some environmental groups.
Ms Braverman said: “I will not bend to protestors attempting to hold the British public to ransom.
“Preventing our emergency services from reaching those who desperately need them is indefensible, hideously selfish and in no way in the public interest.
“This serious and dangerous disruption, let alone the vandalism, is not a freedom of expression, nor a human right. It must stop.”