"It breaks our heart to announced the passing of our founder, Rafael 'Ray' Vega," the Instagram post said on Sunday, adding that Vega "passed away peacefully" the previous day.
The cause of death was not immediately disclosed.
"Ray's parents immigrated with him from Tijuana with dreams of owning a restaurant in L.A.," the statement said. "He grew up at his parents' restaurant on Olvera Street" in downtown Los Angeles.
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Vega launched his namesake restaurant 65 years ago, when he was 22, and he later started other successful businesses in Nevada and California, according to the news release.
He returned to Los Angeles after retiring and was a fixture at Casa Vega for decades.
He is survived by his wife Charleen and children Kelly, Robbie and Christina.