Officers are searching 18 premises in London and one in Stoke-on-Trent.
The Met Police said it was part of an ongoing inquiry into Islamist-related terrorism and not in response to any immediate threat to the public.
Mr Choudary is the former UK head of the Islamist group al-Muhajiroun or Islam4UK, banned in the UK in 2010.
The arrested men, aged between 22 and 51, are being held at police stations in central London.
by Dominic Casciani, Home Affairs correspondent
Anjem Choudary is a deeply controversial Islamic figure, a man who many Muslims despise because they believe he causes enormous damage to their position in British society.
Alongside another now-banned cleric, he once spearheaded al-Muhajiroun, a group that argued that the West is fighting a war against Muslims and Islam.
When the government banned the group, some of its former members founded new organisations, including Islam4UK and Muslims Against Crusades - which were also later banned.
The latter group's protests against British soldiers returning from Afghanistan, led to counter-protests and the subsequent formation of the English Defence League.
Mr Choudary has always denied allegations that he has either incited or glorified acts of terrorism.
In a statement the Met said the men were being held on suspicion of being members of a proscribed organisation, supporting a proscribed organisation contrary to Section 11 and 12 of the Terrorism Act 2000 and encouraging terrorism, contrary to Section 1 of the Terrorism Act 2006.
Police said a number of residential, business and community premises are being searched; 11 in east London, one in west London, one in north-west London and five in south London.
A residential property is also being searched in Stoke-on-Trent.
The arrests were carried out by the Met's Counter Terrorism Command (SO15).

Jacob Brentnall drove to Manchester from his home in Nottingham after midnight when he read about the bombing in the news and on social media.
After giving a young woman a lift across the city he drove a family of three to Leeds, before returning home.
The 21-year-old then turned up for work in Derby despite getting no sleep.
Mr Brentnall said the attack made him feel "sick to my stomach" but it had been heartening to see people pulling together.
"I saw lots of other people tweeting to ask if people needed a place to sleep or anything like that, or if people needed lifts," said Mr Brentnall, who works as an engineer.
"I was under the assumption people would need help and I was in a position to be able to help, I guess it was as simple as that.
"Although something this traumatic has happened, everyone has been capable of pulling together and doing what needs to be done."
He said the family he took to Leeds were visibly "shook up".
"The father said they were out of the immediate area but it was still quite traumatic for them," said Mr Brentnall.
"The mother and daughter were asleep within a couple of minutes and the dad was pale all the way back. He was still in shock.
"They were very grateful and couldn't say thank you enough."
Mr Brentnall also praised the work of the emergency services.
"They were on it straight away," he said.
"Everyone was running away from it but they were running to it. I've got to take my hat off to them."

Betsi Cadwaladr health board has suggested downgrading services at one of the area's three district hospitals due to a staffing shortage.
A legal challenge blocked the plan to downgrade maternity care at Glan Clwyd Hospital in Bodelwyddan, Denbighshire.
That prompted the consultation, which includes a series of public meetings.
Residents are unhappy with the plans, suggesting removing the service at hospitals like Wrexham Maelor and Ysbyty Gwynedd in Bangor will mean women having to travel further for care.
However, bosses said any changes would be temporary and are needed to ensure the safety of mothers and babies.
A dedicated health board website was launched on Monday to collate public reaction to the options, which also includes retaining all services.
Several public meetings are due to take place in September.
Nine men, including the radical Islamist preacher Anjem Choudary, have been arrested in London on suspicion of being members of a banned organisation.
[NEXT_CONCEPT]
A man has described how he felt compelled to drive 200 miles in the middle of the night to help people affected by the Manchester attack.
[NEXT_CONCEPT]
A consultation about plans which could see consultant-led maternity care withdrawn from a district hospital in north Wales has begun.