The police said several of its vehicles, alongside those of the coastguard and Border Force, were damaged during the disruption, which lasted until the early hours of Monday.
It added that a small number of officers were treated at the scene for injuries, but no-one in attendance was seriously injured.
Rowlinson said: “We have been consistently clear that violence and criminal damage have no part in peaceful protest and we will investigate incidents like this thoroughly and take robust action against those responsible.
“Clearly events on Sunday evening were not peaceful protest, rather violent public disorder, and this will not be tolerated as we work to keep our wider communities in Hampshire and on the Isle of Wight safe.”
He also pointed out the force will not tolerate abuse aimed at police or partner agencies online.
This comes after RNLI volunteers were targeted on social media.
“We will work with our colleagues across policing to address any online threats that are made,” Rowlinson said.
“This arrest also sends a clear warning to anyone intent on causing disruption and disorder at any future events. If you break the law we will take action against you and where it is feasible to do so seek a prosecution.”
The disorder in Portsmouth followed a separate anti-migrant protest at the Port of Dover the day before.