“The suspects were arrested in Alexandra with the help from the members of the community,” Lieutenant Colonel Lungelo Dlamini said.
“Several exhibits that may be used as evidence were seized during the arrests.”
The group was arrested on Sunday evening.
The 35-year-old Mozambican national Emmanuel Sithole was stabbed in Alexandra on Saturday morning and later died in hospital.
The three are expected to appear in the Alexandra Magistrate’s Court on Tuesday on charges of murder.
Dlamini said a manhunt for a fourth person was continuing.
On Sunday, Gauteng police announced it was offering a reward of up to R100 000 for information that may lead to the arrest and conviction of those who killed Sithole.
Police spokesperson Lieutenant Colonel Lungelo Dlamini said a manhunt for a group of four men has been launched.
Dlamini said police were still investigating whether his death was related to xenophobia, saying it seemed to have been related to an argument between a street vendor and a customer.
“While police are also investigating the motive for the killing, witnesses allege that the victim was a street vendor and selling cigarettes,” Dlamini said in a statement.
“Suspects approached him and took his goods without paying and thereafter an argument ensued. He was then confronted by one of the suspects who was wielding a knife.”
Sithole was stabbed and taken to a local clinic where he later succumbed to his wounds.
“The ruthless killers of Emmanuel Sithole will face the full might of the law and we are calling all the community of Alexandra to take a stand against criminal elements and help the police to bring them to book,” Major General Vincent Leshabane said.
“Any information will be treated as anonymous and people who know the whereabouts of the suspects should come forward without fear.”