Michel told Belgian television that the arrests were linked to "suspect vehicles" identified during the investigation by French police into the attacks that killed at least 129 people.
The possible link to the new Paris attacks raises fresh fears that Belgium is becoming a hotbed of militancy, coming just months after connections emerged to the Charlie Hebdo attacks and August's attempted attack on an Amsterdam-Paris train.
He separately told RTBF television: "It is believed or suspected that one of these people was in Paris last night."
The Belgian government would consider further security measures, Michel added.
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The Paris prosecutor said that one of the vehicles used in Friday's attacks in the French capital was registered in Belgium and hired by a French national living in Belgium.
Belgian Justice Minister Koen Geens said separately on RTBF television that the arrests in the capital's down-at-heel Molenbeek neighbourhood "can be seen in connection with a grey Polo car rented in Belgium" found near the concert hall in the French capital where scores of people were killed.
In Paris, several witness reported that some of the attackers arrived in a vehicle with Belgian license plates.
The Belgian federal prosecutor said authorities had now opened a formal terrorism investigation.
"The investigation is opened into a charge of terrorism and participation in the activities of a terrorist group," the federal prosecutor's office said.
Belgian media reported that three people were arrested during the raids, but the number was not confirmed officially.
RTBF earlier reported up to three raids as its website ran a photograph of a man with what looked like a black blindfold as the police put his hands behind his back and handcuffed him.