The tunnels near Ebbsfleet International station in Kent were inundated as the Met Office issued weather warnings for rain, snow and ice across large parts of the country.
Eurostar, which runs services from London to Paris, Brussels and Amsterdam via Ashford, midway between London and the southern English coast, apologised to customers for the disruption.
Posting on X, formerly Twitter, Southeastern Railway said: "No highspeed trains are expected to run today between St Pancras and Ashford International.
"We are working to fix the flooding in the tunnels."
In a statement, Southeastern added that "flooding between Ebbsfleet International and London St Pancras International means that all lines are blocked.
"Disruption is expected until the end of the day."
It said flooding had affected both railway tunnels near Ebbsfleet, meaning both tunnels are closed.
"This means no trains can run between London St Pancras International and Ebbsfleet International," Southeastern added.
The disruption comes after French unions ended a wildcat strike that had stranded holidaymakers and held up freight just days before Christmas.
The surprise walkout by workers that blocked the tunnel sparked hours of chaos at rail hubs in Paris and London.
Eurostar train services resumed on December 22 after an agreement was reached.
Eurotunnel unions said negotiations had yielded "results that satisfy us".
Eurostar is owned 55.75 percent by French state-owned SNCF Voyageurs.
It almost went bankrupt during the Covid-19 pandemic but was saved with a 290-million-euro ($320.6 million) bailout from shareholders including the French government.
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