The incident, which was captured on video, happened Wednesday morning in Torrance's Wilson park.
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It was reported to city officials and the Torrance mayor said police were investigating and "Conduct like that displayed on the video cannot be tolerated."
The incident began as a woman was filming her workout in the park.
She was exercising on a set of steps at the park when the other woman walked by and apparently bumped her. "Jesus," the exercising woman muttered. That was enough to set off the older woman, who then started on a tirade that lasted for several minutes.
"Listen to me. We don't play games here anymore. Next time you talk to me like that you're going to get your ass kicked by my family. They're gonna (expletive) you up."
Then she complained about her using the stairs.
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"This is not just for you. Get the (expletive) out of this state. Go back to whatever Asian country you belong in."
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"You (expletive). This is not your place, this is not your home. We do not want you here. Put that on Facebook. I hope you do. Because every (expletive) person will beat the crap out of you from here on out. Don't you ever say oh Jesus to me when I want to use the stairs you little (expletive)."
She keeps going and then as she's walking away, she adds a kicker: "Who wears black in California sun? Who the (expletive) wears black. Are you an idiot, you wear black in California sun? Seriously?"
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The incident was reported to city officials.
Her friend who tweeted video of the incident wrote: "My friend was threatened in Wilson Park in Torrance, California today while she was working out in a public park by a Karen. She now does not feel safe to exercise in the park because of this. This is infuriating."
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Torrance Mayor Patrick Furey said the city is aware of the incident and police are investigating.
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"Public safety is a high priority in the City of Torrance," Furey said. "And, all visitors to our open spaces should always feel safe and free to exercise while practicing social distancing without conflict.
"Conduct like that displayed on the video cannot be tolerated."
"We strive to deliver essential services to our community with integrity, honesty and respect for all users."
Since the video was posted on social media Wednesday, it has been viewed tens of thousands of times.
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One of the original videos can be seen here on Twitter. Caution: contains graphic language.