"Today's summit is cancelled. For now, no new date has been set," the source told AFP on condition of anonymity.
"The next step is for the entire EU to be able to sign the agreement."
European Council President Donald Tusk had said early Wednesday that Canadian Prime Minister Justin Trudeau could still come to Brussels on Thursday for a summit to sign the deal, which has been seven years in the making.
The Belgian federal government has reported that it was near a consensus that would allow it to overcome objections from Belgium's French-speaking communities.
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Belgium has effectively blocked the deal, which must be endorsed by all 28 EU member states.
Brussels said it needed still more time to iron out technical issues before it could throw its support behind the Comprehensive Economic Trade Agreement (CETA).
With no agreement in sight, Trudeau's office said overnight that he had postponed plans to travel to Brussels, adding the "Canadian delegation will not be traveling to Europe tonight.
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