"Three guys were picked up but we are still busy questioning them at this stage," he told Sapa.
"They haven't yet been linked to the crime."
Byleveld, who is the director of the Organised Crime Unit, said he was unable to reveal where they found the suspects.
"We can't disclose more than that at this stage," he said.
The woman, who had not yet been identified, was found inside a burning suitcase on the bank of a stream in Pretoria on 4 July.
Sunnyside police spokeswoman Eveline Hardaker on Monday confirmed that the victim's head had still not been found.
A day after the discovery of the suitcase, the woman's dismembered arms and legs were found wrapped in plastic in a rubbish bin.
Sapa
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