Elizabeth Pena's manager, Gina Rugolo, has said that the Modern Family actress died of natural causes after a brief illness.
No other details were provided.
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Ugly Betty actress America Ferrera paid tribute on Twitter, writing: "Heartbroken to hear the news of Elizabeth Pena's death. She was such a light. So glad I knew her. So sad she's gone."
Eva Longoria added: "Rest in Peace Elizabeth Pena...you paved the way for so many of us!!"
Zoe Saldana also tweeted a tribute to Elizabeth, writing: "My heart is broken!!! My prayers are with you and your family. We will miss you #ElizabethPena"
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Elizabeth, who played the mother of Sofia Vergara's character Gloria in the hit show, also starred in films including Lone Star, The Incredibles, Down And Out In Beverly Hills, and La Bamba.
She also appeared in TV shows such as LA Law, Dream On, I Married Dora, and Resurrection Blvd.
Elizabeth most recently appeared on the El Rey Network drama "Matador."
"She was a role model, a truly extraordinary performer and an inspiration in every sense of the word," the network said in a statement.
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"Our thoughts are with Elizabeth's family and friends during this difficult time. She will be deeply missed."
She is survived by her husband, two children, mother and sister.