Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
"We've noted with concern the political reaction emanating from Zimbabwe, including perceived threats against Nando's Zimbabwe's management, staff and customers," the company said.
On Tuesday a militant youth group loyal to Zimbabwe President Robert Mugabe called for a boycott of Nando's because of the ad.
Nando's SA said it had taken these threats very seriously and would no longer flight the TV commercial as part of its festive season campaign.
"We feel strongly that this is the prudent step to take in a volatile climate and believe that no TV commercial is worth risking the safety of Nando's staff and customers."
The commercial shows Mugabe dining alone at Christmas, his empty table set for departed dictators, including Muammar Gaddafi.
To the soundtrack of Mary Hopkins hit song 'Those Were the Days', the commercial shows an actor playing Mugabe reminiscing about his times with former dictators. It portrays him and Gaddafi engaging in a water pistol fight, AND with Gaddafi wielding an AK-47 rifle.
Mugabe also makes sand angels with Iraq's Saddam Hussein, sings karaoke with Chairman Mao, and holds overthrown Ugandan dictator Idi Amin astride a tank.
The head of Nando's Zimbabwe franchise said it was not told of the SA TV and press campaign.
It is an offence under Zimbabwean law to insult Mugabe or undermine the authority of his office.