Footage shows two men accosting Vuyo Mvoko, from the national broadcaster SABC, who was outside a Johannesburg hospital to report on the arrival of Zambia's president for medical tests.
Mr Mvoko later said one of the muggers threatened him with a gun when he did not want to give up his mobile phone.
The robbers appear unconcerned by the presence of the camera.
Shortly afterwards, Mr Mvoko, who is a contributing editor for the national news channel, tweeted that he was safe and sound and posted a link to a video of the mugging, which has gone viral.
Police said the robbers took laptops and mobile phones and that officers were investigating in the incident.
"Hopefully someone will be able to identify them and get them arrested," Mr Mvoko told the BBC's Newsday programme.
He said it took him a while to realise what was happening as it was less than a minute till he was due to go live near the Milpark Hospital.
"I couldn't understand why they'd walk right in front of the camera because the light is on and they could see that - and our car is branded, so they could see that this is a live broadcast."
The thieves told him to hand over his phone, which he said was in his hand.
"Because I wasn't giving him the phone, he then called the other one who had a gun, and said: 'Dubula le nja' [Shoot this dog]," Mr Mvoko told SABC.
At this point he said another member of the team screamed at him to hand over the phone, which he did.
The BBC's Pumza Fihlani in Johannesburg says Milpark is a relatively quiet area, not normally associated with crime.
The SA National Editors' Forum (Sanef) has condemned the mugging.
"Every South African lives with the reality of crime, but to see thugs brazenly ignoring television cameras and robbing media workers in the course of their work, yet again brings home the level of criminality in our society," a statement from the forum said.
Zambia's President Edgar Lungu, who had collapsed at an event on Sunday, went to South Africa for tests after his doctors found that he needed throat surgery.

Amina Al-Jeffery, 21, had complained her father locked her up in a Jeddah flat, which he has disputed.
But the High Court was told on Friday that a face-to-face meeting with Ms Al-Jeffery's solicitor had not happened due to passport delays.
The case has now been adjourned until February.
In August, Mr Justice Holman said her father had to "permit and facilitate" his daughter's return to England or Wales by 11 September, but she has not returned.
A further hearing was told that restrictions on Miss Al-Jeffery had been eased.
But the judge said he wanted to hear the outcome of a meeting with the woman's solicitor Anne-Marie Hutchinson to resolve the issue "once and for all".
However, the High Court was told that meeting has still not taken place as Irish national Ms Hutchinson required a new passport to accommodate travel visas.
The court was told there was a backlog in passport applications following June's vote to leave the EU.
"There you have it. The reach of Brexit has even impacted on progress in this case. Who would have foreseen it?" said the judge.
One of South Africa's best known TV journalists has been mugged on camera as he waited to go on air.
[NEXT_CONCEPT]
A post-Brexit vote surge in Irish passport applications has hit the case of a Swansea woman claiming to be held in Saudi Arabia against her will.