The South Australian police commissioner has granted permission for a Black Lives Matter protest to proceed in Adelaide.

Up to 4000 people are expected to gather in Victoria Square on Saturday before marching through the city in support of the global calls for justice for US man George Floyd, who died while being arrested in Minneapolis.

Commissioner Grant Stevens says the exemption will allow the event to go without breaching COVID-19 restrictions but those taking part must still be mindful of their own health and the health of others.