The incident happened mid-afternoon on Tuesday 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 remerge seconds later with the officers in tow, forcing them into the back of the vehicle.
They lock the van and then hurry off. The entire robbery takes less than a minute.
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. No injuries were reported,” said Malila.
Three of the suspects were arrested and three firearms confiscated, including the two the gang had just stolen from the police.