The masked gang dressed like police and used two vehicles with blue lights in their raid on Monday.
They took the cache of stones and sped off, a spokeswoman for Brussels prosecutors' office said.
Police found a burnt-out vehicle close to the airport later that night and said they were still looking for clues.
The heist was estimated at some $50 million (£32.3m) in diamonds, said Caroline De Wolf, of the Antwerp World Diamond Centre. She said: "What we are talking about is a gigantic sum."
An airport spokesman said the robbers made a hole in the fence and drove up to the Swiss passenger plane, which was ready to leave. The thieves got out of the car, flashed their weapons and took the jewels from the hold.
They drove off through the same hole in the fence, completing the theft within minutes, he added.
The spokesman could not explain how the area could be so vulnerable to theft.
The flight, bound for Zurich and operated by Helvetic Airways, was cancelled.
The airline declined to comment on the heist, citing the ongoing investigation.
Philip Baum, an aviation security consultant in Britain, said the robbery was worrying not because the fence was breached, but because the response did not appear to have been immediate.
He said: "It does seem very worrying that someone can drive two vehicles on to the airport, effect the robbery, and drive out without being intercepted."