The footage, filmed by a witness and posted on Facebook and YouTube, showed two officers manhandling the suspect, with the help of two uniformed private security guards.
A security guard ripped the shirt-less man's trousers off and then a police officer repeatedly punched and kicked the man in the groin. Another officer held the man by the neck.
Police spokesman for the Western Cape Province Colonel Tembinkosi Kinana said he was "horrified" at seeing the video and that internal investigations had been launched.
"We ...Condemn the behaviour witnessed in the video in its strongest terms," he said in a statement, but did not state when the incident took place.
But the opposition Democratic Alliance (DA) which governs the city and its surrounds, suggested the "vicious attack" took place yesterday.
"What was even more disturbing is that police aggressively manhandled, pushed, choked, punched and kicked him repeatedly," said a DA lawmaker Dianne Kohler Barnard.
South Africa's police are frequently embroiled in allegations of brutality, yet prosecutions rarely occur.
"People living in South Africa are tired of living in fear of both criminals and a handful of thuggish police officers," said the DA's Barnard.
South Africa's police force has come under intense scrutiny since shooting dead 34 striking platinum miners in August 2012.
Nine police officers stand accused of dragging a Mozambican taxi driver behind their van and then beating him to death in custody last year. Their trial is due in May this year.
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