A shopper recorded the incident inside the store on Friday.
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The woman in the video was angry after being questioned about why she was not wearing a mask.
Los Angeles residents are required to wear face coverings when out in public and inside stores and other businesses to help stop the spread of COVID-19.
Other shoppers reacted to the video.
"I feel a little bad that people are getting shamed and she has a medical condition so she can't wear a mask. On the other hand, we know now that the mask is helping to stop the spread, so we should, especially when we're in lines and in places, we need to be more mindful," said shopper Sigrid Matthews.
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"I think you should still wear a mask just for the safety of others, especially for the elderly and kids," said shopper Jessica Govea.
KABC-TV reached out to Trader Joe's for comment about the incident but didn't immediately receive a response.
Man captured on video refusing to wear face covering at Runyon Canyon