"The case has been referred to the Hawks," said Lt-Col Katlego Mogale.
She dismissed a Beeld report that the mastermind of the shootout was arrested.
"Maybe they [the Beeld] should shed light on this case to investigators. I don't know about that."
She said no other arrests had been made.
"Only two suspects are under police guard at hospital, and that is tantamount to being arrested."
Hawks spokesman Hangwani Mulaudzi could not immediately be reached.
Seven people were injured in a shoot-out at the Bedford shopping centre in Bedfordview, east of Johannesburg, on Thursday.
Three customers, two security guards and two robbers were injured and taken to hospital.
Mogale could not provide an update on their conditions on Friday.
On Thursday, police said the security guards were collecting cash inside the centre when they were confronted by a group of armed men.
"A shooting ensued between them, with some customers caught in the crossfire. An undisclosed mount of money was taken by some of the suspects," Mogale said at the time.
The 'Ultimate Family Townhouse' is three stories high and the most expen...The Drive with Rob & Roz 9 hours ago
Fans are divided after learning more about the singer's bath time routin...The Drive with Rob & Roz 10 hours ago