Her nephew, Latino Review writer Mario-Francisco Robles, confirmed the news in an obituary posted on the site.
He wrote, "The actress, with a professional career spanning nearly 40 years, left us on the night of October 14 at Cedars-Sinai Medical Center in Los Angeles."
Peña was best known for her roles in La Bamba and Down and Out in Beverly Hills. Most recently, she also enjoyed a recurring role on ABC's hit series Modern Family, where she played the mother of Sofia Vergara's character Gloria.
According to Deadline, Peña also played the mother of the lead character in Matador, a new series on the El Rey Network.
The publication reports that the El Rey Network issued the following statement about her death: "We are deeply saddened by the passing of our friend and colleague, Elizabeth Peña. She was a role model, a truly extraordinary performer and an inspiration in every sense of the word. Our thoughts are with Elizabeth's family and friends during this difficult time. She will be deeply missed."
Peña also will be missed by many in Hollywood. Celebs have already paid their respects to the late actress via social media.
Rest in Peace Elizabeth Pena...you paved the way for so many of us!! http://t.co/IiGf6JuxGf— Eva Longoria (@EvaLongoria) October 16, 2014
Elizabeth Pena...a ferociously funny, fierce and singular actress. A beautiful woman who has gone way too soon... I miss you already - RIP— Debra Messing (@DebraMessing) October 16, 2014
My heart is broken!!! My prayers are with you and your family. We will miss you #ElizabethPena –ZS— Zoe Saldana (@zoesaldana) October 16, 2014
Elizabeth Pena , May your beautiful soul " Rest in Peace " with love and respect— George Lopez (@georgelopez) October 16, 2014
The entire cast and crew are very sad to say goodbye to one of our Modern Family members. RIP to the beautiful & talented #ElizabethPena.— Jesse Tyler Ferguson (@jessetyler) October 16, 2014
Steve Levitan, Modern Family's co-creator and executive producer, also paid tribute to the late star via Twitter.
We were so sad to learn of the passing of Elizabeth Pena. A member of our Family, she will be missed. #RIPElizabethPena— Steve Levitan (@SteveLevitan) October 16, 2014
Our thoughts are with Peña's family and friends during this sad time.
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