The employee, who asked not to be named but who said he has worked at the embassy for over a decade, said the news came as a surprise and that he was awaiting a call to tell him when to return to work.
It was unclear whether the threat was of terrorism in nature.
Security analysts have raised concerns in recent years that southern African countries, with their relatively porous borders, could become a transit point for Muslim extremists.
One of four men convicted of helping carry out the terrorist attacks on the US embassies in Kenya and Tanzania in 1998 that killed 224 people was arrested in South Africa.
Khalfan Khamis Mohamed, a Tanzanian national, was arrested in Cape Town in 1999 and extradited to the US, where he was sentenced to life in prison.
The threat follows concerns in some Western countries over lax security in the provision of identity documents in South Africa, where fake passports and ID books are widely available.
The British government in March imposed new visa requirements for South Africans travelling to the country because of concerns over corruption in the Home Affairs department.
The South African government has vowed to root out corruption.