Media reported on Tuesday that the men were arrested by counter-terrorism officers in the cities of Birmingham, Ipswich and Northampton and in Powys, Wales.
The suspects, aged 22 to 32, were allegedly involved in the commission, preparation and instigation of acts of terrorism, and of being members of the banned National Action group.
National Action is a neo-Nazi organization proscribed as a terrorist group by the UK government.
The group became the first far-right group to be outlawed in Britain last year after the murder of member of parliament Jo Cox, whose killing the group had praised.
British authorities said the arrests were the result of army and police forces’ planning and intelligence operations.
The Ministry of Defense (MoD) confirmed a number of serving army soldiers had been arrested, but did not reveal how many.
“We can confirm that a number of serving members of the Army have been arrested under the Terrorism Act for being associated with a proscribed far right group,” it said in a statement.
“These arrests are the consequence of a Home Office Police Force led operation supported by the Army,” it added.
MoD spokeswoman said, “This is now the subject of a civilian police investigation and it would be inappropriate to comment further.”
“The arrests were pre-planned and intelligence-led; there was no threat to the public’s safety,” West Midlands Police said.
Last month, a senior police chief said the number of referrals to the authorities about suspected right-wing extremists had doubled since the murder of Cox, who was killed in June last year by a loner obsessed with Nazis and white supremacist ideology.
Britain is on its second-highest threat level, “severe”, meaning an attack is highly likely. Suspected extremists have killed 35 people this year in London and Manchester, and a man died in June after a van was driven into Muslim worshipers near a London mosque.