The city says the fine starts at $100 for the first offense and may increase after that.
Mayor Alicia Weintraub issued a letter to the community saying "the complaints coming into City Hall are rising by the day."
A statement on the city's official Twitter account said the new policy applied to circumstances in which an individual is unable to practice physical distancing of 6 feet or more.
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"If you're walking your dog in the neighborhood and there's nobody around, you don't need a mask," the tweet said. "Just keep one with you in case you come upon a friend or a group of people during your walk. And put it on quickly."
Other Southern California cities enforcing a similar rule include Manhattan Beach, West Hollywood, Santa Monica, and Beverly Hills.