The 23-year-old suspect was detained in Rochester under section 12 of the Terrorism Act 2000 by Sectu officers working with Kent Police colleagues.
He is being held at a police station in the Kent area following what officers said was a "pre-planned" operation.
It is not linked to any immediate threat in the UK, they said.
Det Ch Insp Keith Roberts, of Kent Police, said: "I would like to reassure the community that this investigation should have very little impact on local residents.
"Our officers will continue to maintain a presence in the area, offering reassurance to the local community."
Anti-terrorism officers have arrested a man in Kent on suspicion of supporting a banned organisation, the South East Counter-Terrorism Unit (Sectu) said.