South African police arrested more than 900 people during nationwide anti-migrant protests on Tuesday that were mostly peaceful but at times turned violent, with shops looted, police said on Wednesday.

Of 120 marches, 108 were peaceful while 12 required police intervention, deputy national police commissioner Tebello Mosikili told a press conference, adding reasons for the arrests ranged from immigration violations to public violence, harbouring undocumented migrants and robbery.

Police said in a separate statement that one person was shot dead late on Tuesday in Johannesburg's Alexandra township, where residents were looting informal cornershops known as spaza shops owned by foreign nationals.

Police reinforcements were deployed across five of the country's nine provinces overnight, while soldiers were sent to Johannesburg's inner-city Hillbrow neighbourhood, where two people were injured in a shooting.

In the port city of Durban police opened an inquest over the death of a foreign national who allegedly jumped from the eighth floor of a building on the eve of the protests, believing he was being targeted.

Tuesday's marches were organised to mark a "deadline" an anti-immigrant movement had set for undocumented migrants to leave South Africa.

The protests followed months of unrest that have drawn international criticism as foreigners have been driven from their homes and seen their businesses and property vandalised.