The Montreal SPCA is at full capacity after accepting hundreds of animals in the weeks leading up to July 1.
Quebec's moving day is notorious for animal owners abandoning their pets when they move, often because their new apartment owner does not allow animals.
The agency argues no-pet clauses are discriminatory, and have a larger effect on low-income families that cannot afford to be choosy about rent.
That's why the SPCA is lobbying politicians to enact legislation to prohibit such clauses.
"We're talking about hypothetical situations of animals potentially causing damages and everyone is paying the price for it," said Anita Kapuscinska. "People who do take good care of animals could be affected by it and are affected by it and it's something that we don't think is fair."
A petition calling for legilslation signed by 22,000 people was presented to the National Assembly in June.
A spokesperson for CORPIQ, the largest landlord association in Quebec, claimed that a no-pet clause would raise more problems than it would solve.
"Unfortunately there is no way to guarantee that the rules in the building will be respected by the tenant, and if there's a problem that the tenant will find a solution," he said.
Last month the provincial government tabled legislation to change the status of animals in Quebec and to treat them as "sensitive beings" with "biological imperatives" that must be recognized.