The burglary took place on Monday at an office park in Cape Town's northern suburbs.
CCTV footage shows two men entering a room where various team trophies are stored and touching one of them.
They leave it behind and instead steal whisky, five signed Springbok jerseys and eight laptops, along with items from other offices.
In footagewhich has been shared on Xby South African journalist Yusuf Abramjee, one of the burglars puts his gloved hand on a memorial trophy, lifting it slightly, before moving to the cupboards beneath it.
A South Africa Rugby Union spokesperson told the BBC that all its trophies were secure, adding that the World Cup trophies from previous tournaments were in a cabinet, while the Webb Ellis Cup won last month in France was stored in a safe.
The room containing all the trophies was not broken into and no arrests have been made.
South Africa won the Rugby World Cup on 28 October after beating New Zealand in Paris andbecoming the first nation to win the tournament four times.
The country celebrated the winwith a four-day victory tour, where the team travelled to parades across South Africa.
President Cyril Ramaphosa, alsodeclared 15 December as a public holidayto mark the success "in celebration of the Springboks' momentous achievement".
The break-in happened at around 22:00 local time (20:00 GMT) and Western Cape police were told of concerns that the trophy had been stolen.
The police recorded two cases of business burglary after two incidents at the Tygerberg Office Park in Plattekloof.
According to local media,police said that two well-dressed men entered the business park in a white Toyota Corolla.
They then forced open a window on the ground floor to gain entry to the building and began searching for items.
Local media also reported that 60 laptops were taken from another company in the same park.
Correction: This article originally reported that CCTV had shown two men touching the Rugby World Cup trophy during a burglary and has been updated to make clear that they had touched another trophy, with a South Africa Rugby Union spokesperson confirming the trophy won last month in France was stored in a safe.
Burglars have broken into South Africa Rugby Union's headquarters, however the World Cup trophy was not taken.