Television images showed large crowds of migrants trying to board waiting lorries. Others were held back by riot police.
Around 400 workers blockaded the port of Calais to protest restructuring at its MyFerryLink division, the Syndicat Maritime Nord trade union said. Shipping was halted early in the day and both Eurotunnel and Eurostar later suspended their services because of the disruption.
"Traffic in the tunnel is suspended because of burning tyres, which are the result of port workers," a Eurotunnel spokeswoman said of an incident at the terminal entrance.
The union opposes plans by Eurotunnel to sell two of MyFerryLink's three passenger vessels to Denmark's DFDS and convert the third to freight, cutting jobs.
The day of action was due to end at 7 pm local time (1700 GMT) but Eurostar said it had been informed by Eurotunnel that the tunnel would remain closed all day. "We expect normal service to be resumed tomorrow," it said in a statement.
Earlier, French strike police were deployed to remove protesters blocking motorway access to the tunnel, which had created a 10-km (six-mile) tailback.
A spokeswoman for Eurotunnel said it understood the concerns of the port workers.
"We hope that there will be suitable job proposals tomorrow," she said of a meeting planned for Wednesday.
A spokeswoman for British Prime Minister David Cameron said Britain was in close contact with French authorities. Britain issued travel advice that said migrants were using the disruption to try to board queuing vehicles.
"There are large numbers of illegal migrants in and around Calais who may seek to enter the UK illegally. Although local police patrols have been reinforced, you should keep vehicle doors locked in slow-moving traffic and secure your vehicle when it is left unattended," the Foreign Office said.
Lorries targeted
"We are seeing the usual phenomenon - some migrants are trying to climb into lorries stopped in traffic jams on the motorway leading to the tunnel," the police press office in Arras said. "They're trying to hide in lorries in particular."
The incident is the latest flare-up involving migrants who have amassed around Calais port, hoping to get into Britain.
That is part of a wider migration crisis facing Europe, the target of tens of thousands of would-be refugees fleeing conflict in the Middle East and Africa or of others trying to escape poverty in their home countries.
The issue is due to be discussed at a summit of European leaders in Brussels from Thursday.
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