Video footage taken by a bystander of the incident, near Johannesburg, has been shown in the local media.
A spokesman for the Police Investigative Directorate said he was “shocked” by the footage.
Rights groups often accuse South African police of brutality.
Local media reported that police initially assaulted the 27-year-old Mozambican, a taxi driver, accusing him of parking his vehicle incorrectly in Daveyton, east of Johannesburg.
The video shows a large crowd gathering, as uniformed policemen tie him to a van, dragging him as they drive away.
‘Police vigilantes’
He was later taken into custody, where he died, local media report.
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The fact that the crowd watched and did nothing to help, some even cheering, is a sad indictment of the state of our society”
Kate LorimerOposition MP
“We are investigating an incident involving the death of a man, allegedly at the hands of the police. We are shocked by the footage which has been released,” Independent Police Investigative Directorate (IPID) spokesman Moses Dlamini was quoted by AFP news agency as saying.
“The circumstances surrounding his death are still allegations… Let’s find out what really happened.”
The opposition Democratic Alliance party (DA) called for the officers involved to be suspended and for a thorough investigation to be carried out.
“The fact that it was police who were the vigilantes in this case shows that we cannot trust the [South African Police Service] to uphold the law,” said provincial parliamentarian Kate Lorimer, AFP reports.
“The fact that the crowd watched and did nothing to help, some even cheering, is a sad indictment of the state of our society.”
Rights group Amnesty International said there was an “increasingly disturbing pattern” of police brutality in South Africa.
The IPID had received 720 cases for investigation, including suspicious deaths in police custody, from April 2011 to March 2012, said Amnesty’s southern Africa director Noel Kututwa, AFP reports.
South Africa’s police commissioner Riah Phiyega condemned the incident.
“The matter is viewed by the National Commissioner in a very serious light and it is strongly condemned,” she said in a statement.
The police department did not confirm if the officers involved in the incident had been suspended, AFP reports. Mr Dlamini said the IPID did not have the power to suspend the officers.
“We can only investigate and recommend suspension, we have no power to say that they should be removed from their jobs,” he was quoted as saying.
There was outrage last August when police shot dead 34 striking miners at the Marikana platinum mine in South Africa’s North West province.
A judge-led inquiry appointed by President Jacob Zuma is investigating the shooting.