He is reported to have died in custody later. President Zuma called the incident "horrific" and "unacceptable".
"No human being should be treated in that manner," Zuma added. He said police must operate within the law.
Human rights groups have often accused South African police of brutality, reports the BBC.
South Africa's police watchdog is investigating the footage taken by a bystander of the incident near Johannesburg. It has been widely shown in the media.
Reports say police initially assaulted the 27-year-old 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.
He was later taken into custody, where he died, local media has reported.
Independent Police Investigative Directorate (IPID) spokesman Moses Dlamini said his organisation was investigating the incident and that it too was shocked by the footage.
The opposition Democratic Alliance party (DA) called for the officers involved to be suspended and for a thorough investigation to be carried out.
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.
Police have not conformed if the officers involved in the incident had been suspended, AFP reports. Dlamini said the IPID did not have the power to suspend the officers.