The arrests were made in Barnett and Hilda streets in Hatfield at about 11am. The suspects had been on the run after committing another crime on Saturday.
Metro Police spokesperson Senior Superintendent Isaac Mahamba said the vehicle's original number plate had been replaced.
The suspects, aged 24, 32 and 37, are facing charges of house robbery, attempted murder, possession of an unlicensed firearm and ammunition, as well as possession of a hijacked motor vehicle.
Mahamba said two charges were opened in Limpopo and the others yesterday in Pretoria.
“Between May 18 and 19, three suspects went to a house in Limpopo and committed house robbery and took a VW bakkie, a firearm, R4000 and bank cards and went to withdraw R5000 from the victim's account.
“On Saturday night they went to a pub in Limpopo and an argument ensued between them and a man believed to be the owner of the car.
“They shot him, and his brother rushed him to hospital. Unfortunately they were involved in a car accident on their way there, and we are yet to confirm their current state with the hospital,” he said.
Mahamba said the suspects travelled from Limpopo to Tshwane in the same car. By then, they had removed the original number plate of the car and replaced it with a GP one.
“We received information that these guys were coming to Pretoria, and our officers heard on the radio that the same car they were looking for was parked at a McDonald's outlet in Colbyn.
“When they arrived, they saw a car moving away and followed, while calling for back-up from the SAPS. They managed to stop the car and arrest the men,” he said.
Of the three suspects, two are from Limpopo and the third a Zimbabwean. Their crimes were committed in Bogom and Ga-Mamabolo in Limpopo.
The three are in police custody and expected to appear in the Pretoria Magistrate's Court soon.
“They will appear in court soon after we have combined all the dockets,” Mahamba added.