All Eurostar trains due to cross Belgium on Monday will also be cancelled.
The Belgian rail network will be shut from 10pm on Sunday (2100 GMT) until 11.59pm on January 30th, the two high-speed rail operators said.
"It's almost certain that there will not be a single Eurostar running across Belgium on Monday," said a spokesman.
Travellers on Eurostar trains between London and Brussels -- where European Union leaders are also staging a summit on Monday -- can take replacement buses between Brussels and Lille near the French border, he added.
Passengers are advised not to travel and to check for updates covering London departures timetabled for late on Sunday evening. Tuesday's services are expected to run normally, he said.
Eurostar and Thalys each advised passengers with tickets that they may be reimbursed, Thalys spelling out for the Sunday and the Tuesday also.
Thalys said there will be a "total interruption" of traffic "right through the day," with a risk of delays also flagged for Sunday evening and Tuesday morning, it said.