The 34-year-old, who was detained on Wednesday in Birmingham, can be kept in police custody until the evening of 23 November.
He was arrested on suspicion of "the commission, preparation and instigation" of acts of terrorism under Section 41 of the Terrorism Act 2000.
A search of a property in the city has been completed.
West Midlands Police said the arrest was planned and intelligence-led and there was no threat to the public's safety.
More time has been granted to question a man held on suspicion of terrorism offences.