This would be like the El Paso city council blocking the U.S. from signing a treaty.
An emotional Canadian Trade Minister Chrystia Freeland left the talks in Brussels, saying the EU was "not capable" of signing a trade agreement.
Belgium, the only country blocking accord, needed consent from the regional parliament of Wallonia.
The wide-ranging deal, seven years in the making, was to be signed next week.
Speaking outside the seat of the Walloon government, Ms Freeland told reporters: "It seems evident for me and for Canada that the European Union is not now capable of having an international accord."
One very obvious lesson from this impasse is that it is going to be difficult for the European Union to implement trade and investment deals, perhaps with anyone.
On the other hand, negotiating an agreement with other countries outside the EU should become easier. To put it bluntly, the British government won't need to care what the Walloon parliament thinks.
THIS IS CANADA:
THIS IS THE EU: