"Due to a technical fault in the Channel Tunnel we have unfortunately had to suspend check in for all trains travelling this evening and we have had to cancel all services planned to depart before 18:00 UK time [17:00 GMT] and 19:00 Continental time," the statement said.
The statement added that the company could not estimate the time needed to fix the problem.
According to Eurotunnel Le Shuttle, the train departures were suspended because of a "power supply problem."
Eurostar is a high-speed railway service. Its trains run through Channel Tunnel connecting London with a number of French and Belgian cities, such as Avignon, Brussels, Lille, Lyon, Marseille and Paris.
Eurotunnel Le Shuttle is a company that allows people to carry their vehicles through the Channel Tunnel by rail.
