"It [the investigation] is a very lengthy process and we are still busy with it," Brigadier Selvy Mohlala said.
Earlier, he said the three had not been linked to the Mthembu shooting, but later clarified the investigation was continuing.
No one else had been arrested for Mthembu's shooting and other lines of inquiry were being followed.
Mthembu was shot and wounded on Sunday evening, while withdrawing money from an ATM on Mandela Street, Witbank.
The following evening, three people were arrested in Tzaneen, Limpopo, in possession of suspected stolen property including a laptop, cellphones and bank cards. Police questioned them to determine whether they were involved in Mthembu's shooting.
On Wednesday, Mohlala said the three would appear in court in Limpopo later on Wednesday and then be taken to Mpumalanga.
On Monday evening, ANC spokesman Zizi Kodwa said Mthembu got into a scuffle with the armed robber and a shot was fired. The bullet grazed his cheek and hit him in the shoulder.
Mohlala said after the shot went off the armed man and three accomplices went to Mthembu's car. Four of Mthembu's friends were waiting in the car. They robbed Mthembu and his friends of their money and cellphones.
On Tuesday, Kodwa said Mthembu was recuperating in a Witbank hospital's intensive care unit.
"He is in good spirits and talking."
(File photo: Gallo images)
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