The incident happened mid-afternoon yesterday while the officers stopped for lunch at a busy roadside food stall in a northern Johannesburg township, said a police spokesman.
The robbery was caught on the closed circuit television camera of a nearby business.
The footage shows four men casually walking past the police van and then disappearing from view beneath a tarpaulin where the officers were lunching.
They reemerge seconds later with the officers in tow, forcing them into the back of the vehicle.
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Police spokesman brigadier Neville Malila said members of the public helped the officers out of the car.
The police then called for backup and a chase ensued.
"The suspects lost control of their vehicle and fired several shots at the police who returned fire," said Malila. "No injuries were reported."
Three of the suspects were arrested and three firearms confiscated, including the two the gang had just stolen from the police.