Mogoeng Mogoeng warned ministers that they would be judged "brutally" if they broke their oaths.
Chief Justice Mogoeng put the ball in the Speakers court.
There was previously speculation that Nkosinathi Msimango might be released from police custody over the weekend due to lack of evidence.
Their lawyers says there's no mention of those 15 stolen computers.
The Office of the Chief Justice was protected by private security guards.
The computers with personal information on every judge were stolen just 16 hours after the Concourt's damning social grants judgment.
A team had been appointed to expedite the processing of the crime scene.