The gang drove into a restricted zone at OR Tambo Airport around 7pm on Tuesday night and headed straight for containers of cash being loaded on to a cargo plane.
A police source told AFP news agency: “They told the security that they were carrying out an investigation and the security (guards) opened the boom gate for them.”
Media reports have said the foreign currency was worth more than $1.5m (£1.2m).
The company that operates the airport – the largest in South Africa – confirmed in a statement that an armed robbery had taken place.
Hangwani Mulaudzi, a spokesman for South Africa’s elite police unit the Hawks, said he could not confirm the value of the money taken.
He told SABC News: “It actually took place in the cargo section of the airport so it’s not the area where you know you will have your normal flights going through to different areas.
“These are national key points and there’s a high level of security as well.
“So that is why we are actually a bit perturbed as to actually how it transpired because we know that there are procedures that need to be followed if one has to go into the tarmac or to any area within the airport.”