The Metropolitan Police has confirmed the man was arrested on suspicion of offences that allegedly took place on Monday 7 January.
Video footage of the arrest now appears to show Goddard being put in the back of a police van by an extremely large number of police officers.
The force said the man arrested was not charged and has been released on bail until early February.
Goddard has been following in the footsteps of campaigner Tommy Robinson in recent months by using social media to stage political stunts and appeal for donations via PayPal.
Ms Soubry, a prominent supporter of a second European Union referendum, was taunted as she was interviewed in Westminster on Monday, and then harangued by a group of men as she made her way back to parliament.
The former forklift driver was involved in a protest in Westminster earlier this week where Soubry was called a "Nazi" and a "fascist".
Politicians from across the House of Commons of voiced their support for Soubry in the face of "abuse" and "intimidation".
James Goddard, one of the leading members of the so-called "Yellow Vest UK" protesters, has been arrested.
James Goddard, the "yellow vest" activist at the centre of controversy over the harassment of MPs and journalists outside parliament, has reportedly been arrested on suspicion of committing public order offences. Police did not confirm whether Goddard's arrest was related to the incident. "He is now in police custody and is being taken to a central London police station".