The 25-year-old man was arrested on the morning of Wednesday, 14 July, at an address in east London on suspicion of encouraging terrorism (contrary to Section 1 of the Terrorism Act 2006).
He was detained under the Police and Criminal Evidence Act (PACE), and taken to a London police station.
He has been bailed to a date in August pending ongoing enquiries.
The investigation relates to Islamist material shared online, and is ongoing.