Belgium has been living under a high threat level since the November attacks in Paris.
"The madness of men is what it is but peace must win over."
The three were taken into custody during a police search in the Brussels district of Uccle on Tuesday.
The statement from prosecutors said the investigation "is continuing actively day and night.''
Perpetrators were "surprised by the speed of the progress in the ongoing investigation'' and decided to rush an attack on Brussels instead.
Airport officials suggested the first flight out was a symbolic victory over those who sowed death and hate.
Police used water cannons when scuffles broke out in front of the Bourse, which has become a symbolic rallying point for people to pay their respects.
Adelma Tapia Ruiz is among the 31 people who died in the attacks.
How companies are responding to the Brussels attack.
The report said two of the men were known to police.