Vehicles were backed up on the A16 and A26 motorways on Thursday morning as about 80 dockers and crane operators stopped work and picketed the terminal in protest at a boat being unloaded by private operators.
Some traffic was diverted to the Channel tunnel.
Union representatives said that no ferries were leaving the port on Thursday morning, although port officials said that some activity resumed during the course of the day.
The strike was likely to continue on Friday if no agreement was reached.
A local court was set to hear an appeal by the dockers' employer, the Nord Pas de Calais region, to have the strikers cleared from the quays on Thursday afternoon.
The dockers are worried that jobs may go if the work, which they usually carry out, is done by outside companies.
"Given that there is not a lot of traffic for the Calais crane operators and dockers and that there is 18 per cent unemployment, we're amazed that the region is asking operators to do the work themselves," said Alain Merville of the CGT union. "We don't understand, it creates a precedent."