MyFerryLink workers walked out for the second time in a week over the sale of its ferries to rival DFDS Seaways.
All services between the Port of Dover and Calais are affected, although DFDS is still sailing to Dunkirk as normal.
A strike on 23 June led to the the suspension of Channel Tunnel services and saw hundreds of migrants try to board UK-bound lorries amid the chaos.
Highways England said Operation Stack - where lorries use part of the M20 to queue for Channel crossings - has been implemented as a result of the latest action.
Kent Police said they were monitoring the latest situation.
Passengers have been advised to contact ferry operators before travelling.
A Eurotunnel spokesman said: "At the moment the strike is affecting the port and ferry services only and all our services are running well.
"We are braced with contingency plans should that change."
Transport Secretary Patrick McLoughlin has chaired a meeting of the government's emergency committee Cobra.
He said: "We're looking at the situation and working with the French government."
Last week's disruption lasted 36 hours and saw blockades at the French port and the Channel Tunnel in Coquelles.
Several Eurostar trains were forced to return to St Pancras. Parts of the M20 in Kent were also closed with lorries waiting to cross the Channel queuing on the carriageway.
In France, the migrants sought to exploit the port strike by attempting to climb on board lorries caught in slow-moving traffic in an attempt to enter the UK.
Prime Minister David Cameron said in the Commons that the scenes were "totally unacceptable" and the strike had played a "key role" in the events. He said more needed to be done to tackle the issue of migrants trying to cross the Channel and it was important to work with France.
MyFerryLink is due to cease operations after 2 July following the sale of its ferries.
Strike action in Calais has led to the closure of the port and suspension of ferry sailings from Dover.