"In connection with a criminal investigation concerning terrorism... 40 persons were taken for questioning. Twelve among them were arrested. The investigating judge will decide on their possible detention later today," the office said in a statement.
"The investigatory results necessitated an immediate intervention. The investigation continues."
Investigators have found links between the Brussels and Paris attackers, some of whom were based in Belgium.
Belgium's federal prosecutor's office said no weapons or explosives were found during the searches, which also involved 152 garage lockups.
A French police couple were stabbed to death outside their home on Monday in an attack claimed by Islamic State. In a video posted on social networks, the Larossi Abballa, the attacker, linked it to the soccer tournament, saying: "The Euros will be a graveyard."
A spokeswoman for Paris public prosecutor Francois Molins said two people close to Abballa would meet a judge on Saturday.