The 31-year-old was arrested in Norfolk by Metropolitan Police counter-terrorism officers shortly after 06:00 GMT on Thursday.
He was being held for questioning at a police station in central London.
The Met said searches were being carried out at two addresses in Norfolk and one in north London.
The arrest relates to suspected activities overseas, police said.
A man has been arrested on suspicion of fund-raising for terrorism and encouraging support for a banned terror group.