The thieves are said to have driven into a restricted zone on Tuesday evening and taken containers of cash.
Estimates vary but reports suggest that millions of dollars in different currencies may have been stolen.
The company that operates OR Tambo Airport, the continent's busiest, confirmed a robbery had taken place.
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"No shots were fired and no injuries have been reported. The robbers fled‚" Airports Company South Africa said in a statement.
The Hawks, an elite police unit, declined to release details, but has said that a high level investigation by all law enforcement agencies is now under way, the BBC's Milton Nkosi reports.
The police have described the robbery as bearing the hallmarks of an inside job.
A source within the Hawks has described the robbery as looking like "something scripted from a Hollywood movie", South African journalist Graeme Hosken told the BBC's Newsday programme.
The journalist added that the thieves, who used special access passes to get into the airport, knew exactly which containers to take and were careful to get hold of small denomination notes, which are thought to be easier to pass on.
A police spokeswoman, Athlenda Mathe, was quoted by South African broadcaster eNCA as saying she could not comment on "how much money exactly was stolen".
Guards from a private security firm protecting the valuable cargo were stopped by the robbers, who were travelling in a vehicle marked with "police", the TimesLive news website reports.
There have been reports of other high-value cargo robberies in recent years at the airport.
OR Tambo is operating normally and no passengers were affected by the robbery.
Via - BBC