The raid saw the gang of thieves hit a Brinks security truck as its contents were being loaded onto a Swiss aircraft bound for Zurich, it said.
VRT public television initially spoke of the haul being worth 350 million euros ($465 million), but later changed their figures to 50 million euros (roughly Sh5 billion).
If confirmed, the robbery would be one of the biggest diamond heists of all time.
Belgian prosecutors confirmed that a raid had been carried out at the airport but did not specify what was stolen. They were expected to provide more details at a press conference later in the day.
A statement from the airport said the robbers drove through barriers onto the tarmac to get airside on Monday evening.
Reports said no shots were fired, no-one was injured and the heist was completed within a matter of minutes.
One of the vehicles was found afterwards burnt out near the airport, local police added.