The incident happened at Ebbsfleet station in north Kent and involved a Brussels-bound train that had left St Pancras in London at 8.58am yesterday.
Kent firefighters used thermal imaging cameras and located a small electrical fire in the engine compartment.
No one was hurt.
The train was taken out of service and a replacement sent to take the passengers on to Belgium, where they were expected to arrive between 60 and 90 minutes late.
A Eurostar spokeswoman said: "One of our trains going to Brussels had a technical problem. Once the fault was identified, the train was taken out of service and a replacement train sent."
It was the second successive day of disruption for the Channel Tunnel high-speed train company.
The day before, hundreds of Eurostar passengers were delayed after a lightning strike triggered a fire in a building close to the entrance to the Kent tunnel.