The fever has provisionally been identified as an arenavirus, the National Institute for Communicable Diseases (NICD) and the Department of Health said, according to South Africa's SAPA news agency.
"The causative agent of the disease... may be a rodent-born arenavirus related to the Lassa fever virus of West Africa," NICD's Lucille Blumberg told reporters here, SAPA said.
Lassa fever claims about 200 lives every year in Sierra Leone, health officials in that west African country said earlier this year.
Blumberg said tests were carried out by NICD and the Centres for Disease Control in the United States.
The World Health Organisation has also been providing technical assistance in identifying the virus.
Arenaviruses cause chronic infections in certain wild mice which pass the virus along through their urine, potentially contaminating human food or house dust particles.
There was no indication that arenaviruses which could cause disease in humans were present in South African rodents, she said, but added that further tests needed to be done.
Two of the three victims in Johannesburg had come from Zambia.