Liege Airport was also closed due to drones, and similar incidents have recently affected other European airports, including Copenhagen and Oslo.
Defence Minister Theo Francken suggested the incident appeared to be carried out by professionals intent on destabilising the country.
The Minister of the Interior, Bernard Quintin, called for a coordinated national response and asked the prime minister to convene the National Security Council.
Brussels Airport has since reopened, but officials warn that travel disruption and delays are expected to continue into Wednesday.