The men are a 22-year-old from Birmingham, a 32-year-old from Powys, a 24-year-old from Ipswich and a 24-year-old from Northampton.
All four are being held at a West Midlands police station.
The Army confirmed the arrests, and said it had supported the police-led operation.
An Army spokesperson added: "This is now the subject of a civilian police investigation and it would be inappropriate to comment further."
The BBC understands the four soldiers arrested are from Royal Anglian Regiment.
Police said the arrests were pre-planned and intelligence-led, and there had been no threat to the public's safety.
They said they were continuing to search several properties.
The men are being held on suspicion of being concerned in the commission, preparation and instigation of acts of terrorism under Section 41 of the Terrorism Act 2000; namely on suspicion of being members of a proscribed organisation.
Who are National Action?
National Action became the first British neo-Nazi group to be banned last December after Home Secretary Amber Rudd said it was promoting violence and acts of terrorism.
Members and supporters applauded the murder of Jo Cox MP by a white supremacist - and the group had carried out a series of small but confrontational demonstrations in towns and cities throughout England.
One of its most notorious events saw masked members - many of them very young men - gathering outside York Minster to make Hitler salutes.
Since it was banned, detectives have been carrying out more and more investigations into the group which, to all intents and purposes, has organised itself in a similar way to the banned al Muhajiroun network - the extremist Islamist youth movement.
Both have used social media to target young people, attracting them with a simplistic us-and-them message designed to make them angry.
Being a member of - or inviting support for - a proscribed organisation is a criminal offence carrying a sentence of up to 10 years in prison.
There are 71 such groups listed by the Home Office on its register.
It describes itself as a "National Socialist youth organisation" and says its movement is aimed at the "broken right-wing".
The official register says it was established in 2013 and has branches across the UK which "conduct provocative street demonstrations and stunts aimed at intimidating local communities".
Its online material contains extremely violent imagery and language and it condones and glorifies those who have used extreme violence for political or ideological ends, the Home Office says.
That included tweets in 2016 about the murder of Labour MP Jo Cox, who was stabbed and shot by Thomas Mair. One such tweet said there were "only 649 MPs to go".
Ms Rudd called it "a racist, anti-Semitic and homophobic organisation".
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