Abu Haleema, who has posted films online attacking British Armed Forces and vowing never to “submit” to democracy, was detained by Scotland Yard counter-terrorism officers in west London.
He was freed on bail after questioning to allow police investigations to continue.
But presumably in an attempt to prevent allegedly inflammatory postings, he was told to halt his online activities as a condition of his release.
The precise terms of the curbs imposed on Haleema have not been disclosed, but have prompted complaints from his supporters about the suppression of free speech.
The move comes, however, amid increasing concern within Scotland Yard and the Government about the impact of radical content on the internet.
Thousands of pieces of inflammatory content have already been removed from the web by a special police unit set up to tackle extremism, while the Twitter accounts of a number of radicals, including Haleema, were suspended earlier this year.
The action against Haleema, an associate of Anjem Choudary, follows months in which he used social media to support prominent extremists.
Examples include retweeting a message calling for the release of the jailed extremist cleric Abu Hamza.
Haleema has also offered support to Omar Bakri Mohammed, another radical preacher once described as Osama bin Laden’s right-hand man in Europe, who now lives in Lebanon after being barred from Britain.
The Met declined to comment on Haleema’s case or the details of bail conditions, but confirmed that counter-terrorism police had made an arrest in west London last month.
A spokesman added: “Officers from the counter-terrorism command SO15 arrested a 37-year-old man in a west London street on suspicion of encouragement of terrorism contrary to Section 1 of the Terrorism Act 2006.
“He was taken to a central London Police Station and has since been bailed to a date in mid-June pending further enquiries.
The man was detained under the Police and Criminal Evidence Act.”