An estimated 600 people gathered at Westfield in Shepherd's Bush for the so-called "die-in" demonstration.
Police said the arrests were made when a breakaway group assaulted security staff and damaged property.
The protest was in solidarity with rallies in the US prompted by the death of Eric Garner, a black man who died during an arrest in New York in July.
Two peaceful protests were held in west London on Wednesday evening, one inside the Westfield shopping mall and one outside.
It is believed those staging the occupation were asked to move outside, a request that was peacefully complied with, Scotland Yard said.
But, according to a police statement, a group then tried to gain access to the centre and were arrested on suspicion of public order offences and one man was held on suspicion of assault.
The Metropolitan Police said they dealt with the protesters using tactics "including a containment for the purpose of preventing violence and effecting arrests".
Commanding officer Ch Supt Mark Bird said: "We will always work with those that wish to demonstrate lawfully - as the majority of protesters did yesterday.
"However, we will not tolerate the small minority that offer violence or commit other criminal acts, such as that witnessed outside Westfield."
The Met said their inquiries into the incident were continuing.
Mr Garner, 43, was stopped on a street in New York on 17 July on suspicion of selling loose, untaxed cigarettes.
Police officers wrestled him to the ground and he complained he could not breathe as he was restrained in an apparent chokehold. He became unresponsive and later died.
Thousands of people have taken to the streets in the US in protest over his death and that of Michael Brown, 18, who was killed in Ferguson, Missouri on 9 August.
Grand juries in Missouri and New York have decided not to charge the officers involved.
West London protesters held signs carrying the same "Black lives matter" message as seen in US demonstrations.
Police have arrested 76 people who were taking part in a mass protest at a major west London shopping centre.