Organizers say the Civil Code currently considers animals to be movable property and that hurting or abusing them is viewed as tantamount to the destruction of property.
"We believe that animals are not toasters," reads the "Animals Are Not Things" manifesto.
It also states that likening animals to objects also means ignoring the current scientific knowledge.
"Animals' capacity to feel pain is now the object of broad consensus, at the very least when it comes to vertebrates," the manifesto reads.
"We are increasingly discovering cognitive and emotional capabilities in animals that are much more complex than once thought — and this holds true not only for primates, dolphins and dogs, but also for cows, rats, and pigeons."
Sophie Gaillard, a lawyer for the SPCA, said the legal status of animals could be changed in various ways.
In an interview, she said the least constraining would be to give them a "symbolically different status that doesn't really have an impact on the way they are treated."
The most restrictive would be to "grant animals a legal status where they would be treated as people."
While such a scenario may seem far-fetched, Gaillard said companies in Quebec are considered like people when it comes to civil law.
A third option would fall in between, she said.
"Animals could have certain rights but still be subject to ownership," Gaillard said.
"That would mean people could still own them and buy and sell them but that animals would have certain rights that could be used against their owners."
The signatories want Justice Minister Stephanie Vallee to listen to their concerns.
Quebec is considered one of the worst jurisdictions in Canada in terms of animal-welfare legislation.