The proposal would require stores in Los Angeles to obtain their animals from shelters or animal protection agencies.
The council didn't pass the ordinance unanimously, so it will go up for a second vote next week, which will require a simple majority for passage.
The goal is to shut down puppy and kitten mills and reduce euthanizations.
The penalty for a first violation would be $250. The fine would go up to $1,000 for a third strike.
Individuals can still purchase pets from breeders.
City News Service contributed to this report.