His arrest was the result of a joint operation between Wales Extremism Counter Terrorism Unit, North Wales Police and West Midlands Counter Terrorism Unit.
Police say it was planned and intelligence-led, and that there was no threat to the public's safety.
The man is being questioned at a police station in the West Midlands.
An address in Wrexham is subject of an ongoing search.
A 48-year-old man has been arrested in Wrexham on suspicion of terrorism offences.