Lt Gen Dimpane issued a “stern warning” to those who “continue to intimidate, harass and perpetrate violence against foreign nationals”.
“The law applies equally to everyone,” she said.
“No individual or group has the authority to conduct immigration inspections, verify legal status, or remove people from communities.”
When questioned on how some foreign nationals had been treated by anti-migrant protesters, Dube said March and March rejected “any form of violence – we reject any form of anti-law”.
There are more than three million documented foreign nationals in South Africa, according to official figures, which does not account for those in the country illegally.
Several countries, including Ghana, Kenya, Malawi, Nigeria and Uganda, have been organising flights or buses for their citizens to return home in recent weeks.
On Wednesday, the last flight organised by the Nigerian government under its voluntary repatriation scheme, landed in Lagos carrying 306 passengers. More than 1,200 Nigerians have now returned under the programme.
Additional reporting by Makuochi Okafor
