The 21-year-old is alleged to have made comments at an event in Blackpool in March 2016 and on social media as part of the National Action group.
The group, which was banned as a terrorist organisation in December, holds anti-Semitic views.
The Blackpool man is suspected of displaying material likely to incite racial hatred and using abusive words.
Support of National Action was outlawed by Home Secretary Amber Rudd under the Terrorism Act.
The move saw it become the first far-right organisation to be banned as a terror group.
The event in Blackpool, which was organised by right-wing group the North West Infidels, saw anti-Semitic chanting and cheering for Adolf Hitler.
The man has been taken to a Lancashire police station for questioning.
The arrest was made by officers from both Lancashire Police and the North West Counter Terrorism Unit.
A man has been arrested over comments and online posts relating to "right wing extremism", police have said.