"Police today raided the home of the man's parents and confiscated laptops and mobile phones," the Dutch public prosecutor's office said in a statement on Tuesday after the raid in central city of Utrecht.
"He's being investigated for suspected involvement in terrorism," it added.
Belgian security services discovered the Dutch passport of the man after Thursday's raid in the eastern town of Verviers, during which two suspected militants were killed.
He is believed to have fled Belgium for Spain or France.
Spanish media have identified the suspect as Zaid Kouliss, who was reported missing by his parents last year.
A second suspect identified as Abdelmounaim Haddad is also believed to be in Spain and investigators fear the two may try to reach Syria.
The cell was allegedly plotting an imminent attack on Belgian police when it was broken up.
Meanwhile, a 33-year-old Algerian man with suspected links to the jihadist cell agreed on Tuesday to be extradited from Greece wanting to "prove his innocence".
The Islamist attacks which the police claim to have foiled have led to at least 13 arrests in Belgium and in several other European countries.