Eurotunnel services are suspended after a "massive invasion" of more than 100 migrants in the French terminal.
A "large and co-ordinated" group stormed the tracks at Calais at around 12.30am local time (11.30pm BST), Eurotunnel said.
A spokesman said: "It's a massive invasion and intrusion by a very large and co-ordinated group of migrants.
"They are being gathered up by the police authorities."
He added: "It's clearly an organised attack when it comes in such a large number, there are over 100 in this one group.
"They arrived together an in a well-organised manner broke through the fences and all clearly new where they were going."
Services are not expected to resume until at least 10am UK time and passengers have been warned of lengthy delays.
British authorities are working with French police to clear the tracks.
"They are being gathered up by the police authorities and British police," a Eurotunnel spokesman added.
"It's a very co-ordinated and well-managed process but it's a very large group of people and it's dark so it will have to be done very carefully."
He added: "While they are on the track we have, for safety reasons, to suspend the service.
"Once that's done we will be able to restart."
Affected passengers are able to use their tickets on the ferry during the disruption.
"There's nobody (stuck) on trains, there are a small number of passengers affected and customers have gone to the ferry port to continue their journeys," Eurotunnel said.
Eurotunnel has implemented extra security to try to prevent migrants getting onto the tracks.
"Quite probably because the security at the tunnel is strengthening every day, with the new fences being put up, new security installations and additional staff, it's becoming much harder for migrants to get through in small numbers," the spokesman said.
"This looks like quite a carefully co-ordinated and organised attack, possibly to raise the profile of their situation or as last-ditch attempt before the new fences are up."
Thirteen migrants have died trying to reach Britain since the start of the crisis in June.
An Eritrean man in his 20s, was killed on Wednesday and is believed to have been hit by a freight train near the tunnel entrance at around 1am.
Early on Tuesday morning a 20-year-old Iraqi man was crushed to death after apparently sneaking on board a lorry to reach the UK.
The HGV driver discovered the body in the back of his vehicle near Calais port as he inspected his load after he was forced to brake suddenly.
An estimated 5,000 migrants displaced from countries including Syria, Libya and Eritrea are believed to be camped in and around Calais.
At its peak, the number of attempts to board lorries or trains was around 2,000 a night - but that has since fallen.
The crisis in Calais is part of a wider migrant surge in to Europe from countries in North Africa and the Middle East.