A “large and co-ordinated” group stormed the tracks at Calais at around 12.30am local time, Eurotunnel said.
Several Channel tunnel staff and two police officers were injured during the incident, the rail company said. Police are believed to have arrested up to 100 people.
A Eurotunnel 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.
“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 and in a well-organised manner broke through the fences and all clearly knew where they were going.
“They ran through the terminal, knocking some staff to the ground and throwing stones at them. There are some minor injuries to staff and also two police officers. They were treated at the scene by paramedics.”
According to the Eurotunnel website, services resumed at 8.30am UK time and passengers on both sides of the channel were being told to expect delays of about 30 minutes.
British authorities had worked overnight with French police to clear the tracks
. The Eurotunnel spokesman said nobody had been stuck on trains and overnight travellers had continued their journeys by ferry.
Thirteen people have died trying to reach Britain since the start of the refugee crisis in June. An Eritrean man in his 20s was killed on Wednesday after he was believed to have been hit by a freight train near the tunnel entrance.
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 found the body in the back of his vehicle near Calais port while inspecting his load after being forced to brake suddenly.
An estimated 5,000 people 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.
A report about the camp known as the Jungle, home to about 3,000 people, saidconditions there were diabolical, with cramped makeshift tents plagued by rats, water sources contaminated by faeces and inhabitants suffering from tuberculosis, scabies and post-traumatic stress.