Videos posted on social media showed groups of men dressed in black and wearing scarves and balaclavas blocking major roads to the port on Saturday.
Kent Police said it was "aware of a protest currently taking place at the Port of Dover".
"Officers are in attendance and engaging with protesters", police said in a short statement on X.
Councillor Chris Vinson, leader of the Conservative group and the member for Walmer on Dover District Council, said the protest appeared to be "illegal migration-related", but said the demonstrators did not appear to have placards or banners.
"Overnight, clearly what appears to be several hundred masked men wearing black clothing and balaclavas seem to have co-ordinated and loaded into rental vans and then descended on roads leading in and out of Dover with the intent to block them, and that's what they've successfully done, and it's brought the town to a standstill," he told the Press Association.
"There are stacks of people who are stuck in their cars or in their workplaces as a result."
He said he was ot aware there had been any violence.
"Although clearly, having the path of your vehicle blocked by men wearing black paramilitary gear and balaclavas is extremely intimidating, especially when it's not clear why they're there, and the police weren't aware and so haven't been able to warn people in advance and make sure that they are made to feel safe," he said.
"I know people who have worked night shifts in the port who are being prevented from leaving for fears for their safety.
"Women who are in cars feeling intimidated, people stuck in traffic - who obviously are without toilet facilities - queues way back on the A20 and the other approach roads into Dover."
Police did not immediately respond to a Reuters request for information about the nature of the protest and further details.
The Port of Dover said there was an "ongoing public order incident happening around the town of Dover" affecting all routes in and out of the port.
"We are in contact with Kent Police to understand the situation," it said.
P&O Ferries said its sailings were going ahead as scheduled.
"If you miss your booked departure today, we will get you onto the next available," it said on X.
with PA
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