"We want to continue living normally," Michel told a news conference. "The situation is under control."
He added: "We are extremely vigilant, we are monitoring the situation hour by hour and we will continue with determination the fight against extremism, radicalisation and terrorism".
No weapons or explosives were found during the overnight searches, which also involved 152 garage lockups. Flemish public broadcaster VTM said the people arrested were suspected of planning an attack in Brussels during one of Belgium's matches.
Areas where fans watch matches in Brussels were potential targets, as well as other crowded areas such as shopping centres and stations, Belgian media reported.
With the Euro 2016 soccer tournament underway in neighbouring France, Europe is on high security alert.
March's deadly attacks by Islamist suicide bombers in Brussels followed attacks in Paris last November in which 130 people died. Investigators have found links between the Brussels and Paris attackers, some of whom were based in Belgium.
- Reuters, AAP