Disguised as police, they broke through a fence on Monday evening and broke into the cargo of a Swiss-bound plane to take the gems, estimated to be worth $50m (Â£32m; 37m euros).
They escaped back through the same hole. Police later found a burned-out vehicle close to the airport.
Police are looking for eight men, a prosecutors' spokeswoman said.
Caroline De Wolf, of the Antwerp World Diamond Centre, estimated the haul at $50m, saying: "What we are talking about is obviously a gigantic sum."
Earlier reports suggested the figure was even higher - with the Belgian state broadcaster reportedly putting it at 350m euros ($468m).
AFP quoted an unnamed spokeswoman at the same Antwerp centre calling the robbery "one of the biggest" ever.
She said that the diamonds were "rough stones" being transported from Antwerp to Zurich.
Antwerp is the hub of the world diamond trade - about 150m euros' worth of stones move in and out of the city every day, the spokeswoman added.
Brussels prosecutor's spokeswoman Anja Bijnens said the thieves were masked and well armed, and used two black vehicles with police markings.
The forced their way through security barriers and sped towards the Helvetic Airways plane about to take off - forcing open the cargo to reach gems that had already been loaded on.
The thieves took 120 packages - only some of the shipment, she said.
No shots were fired and no-one was hurt. The raid was over in a matter of minutes, and the thieves made off into the night.
They were "professionals", Ms Bijnens said.
Ms De Wolf said the raid was a blow to Antwerp's reputation as a secure and discreet diamond centre.
"This is causing quite some unrest,'' she said, according to AP news agency.
"It was incredible how easy it all went. This is worrying in terms of competitiveness, since other diamond centres are ready to pounce and take over our position.''
An airport spokesman, Jan Van Der Crujsse, could not explain the security breach. "We abide by the most stringent rules,'' he said.
Armed robbers have made off with a "gigantic" haul of diamonds after a rapid raid at Brussels Airport.