Kent Police said it was aware of a protest "currently taking place" at the ferry terminal and was "engaging with protesters".
Traffic has been stopped from going in and out of the port due to the incident.
P&O Ferries said it would get passengers on to the next available sailing if they missed their scheduled crossing.
Traffic is stopped in both directions on the A20, between the A256 York Street and the A2 Jubilee Way in Dover, according to National Highways.
It is reporting four miles (6.4km) of congestion and delays of up to 30 minutes.
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