Some anti-migrant groups had given undocumented foreigners a deadline of 30 June to leave the country and organised marches attended by thousands of people on Tuesday. These were largely peaceful but there were isolated incidents of violence against foreigners.
The South African police say that about 900 people were arrested, mostly for immigration-related offences and looting.
The BBC has asked South Africa’s government for comment on Nigeria’s compensation demand.
Nigeria’s acting high commissioner said he had asked all of those who had left South Africa “to document very accurately those things they were leaving behind in terms of businesses, in terms of even cars, movable and immovable properties”.
Foreign ministry spokesperson Ebienfa told the BBC that all claims would be verified before any formal request was made.
“We have not severed ties with South Africa, we are still engaging them at the highest level, we will sort those details using our usual diplomatic channels,” he said.