"At around 12:30 AM (0400 IST), around 100 migrants forced a closure and the entry of security agents into the tunnel," a Eurotunnel spokeswoman told AFP.
"We have suspended the service."
She said police were at the site and that traffic remained suspended.
Ten people, including seven migrants, suffered minor injuries in the storming of the tunnel, a firefighter at the scene said.
The interior ministers of France and Britain in August signed an agreement to set up a new "command and control centre" to tackle smuggling gangs in Calais, as Europe grapples with its biggest migration crisis since World War II.
Thousands of people from Africa, the Middle East and Asia are camped in Calais in slum-like conditions, and at least 13 have died since June 26 trying to cross over into Britain, where many have family and work is thought easier to find.
