Martin Reynolds, 46, was taken into police custody outside a fundraising event for the far-right party in St Helens at 6pm on Saturday.
Merseyside Police confirmed officers were called to Thatto Heath by a woman reporting that a man had got out of a car and made a derogatory remark towards her.
Mr Reynolds, who is from the Leeds area, was arrested on suspicion of an aggravated public order offence.
Photographs on the BNP's Facebook page show Mr Griffin looking on as Mr Reynolds is led away by police.
On their Facebook page, the party claim the arrest was "politically motivated" and that the police have not revealed why he was arrested.
Police said a probe into the incident was continuing.