Peña's manager, Gina Rugolo, says the actress died Tuesday in Los Angeles of natural causes after a brief illness. No other details were provided.
Peña's career spanned four decades and included roles in films like Rush Hour, Jacob's Ladder and Free Willy 2.
She also appeared on such TV shows as L.A. Law, Dream On, Resurrection Blvd. and Modern Family, where she played the mother of Sofia Vergara's character, Gloria.
She also provided her voice to The Incredibles, the Justice League cartoon series and American Dad.
Peña recently played the mother of the title character on the El Rey Network drama Matador.
"We are deeply saddened by the passing of our friend and colleague, Elizabeth Peña," the El Rey network said in a statement. "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."
She is survived by her husband, two children, mother and sister.
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
Aw...damn. Elizabeth Pena was a wonderful actress and even lovelier person. My thoughts are with her family.— Dana Delany (@DanaDelany) October 16, 2014
Rest in Peace Elizabeth Pena...you paved the way for so many of us!! http://t.co/IiGf6JuxGf— Eva Longoria (@EvaLongoria) 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 Peña was wonderful in everything she did. She shone so bright. An incredibly gifted actress. I loved her. Rest in Peace.— Martha Plimpton (@MarthaPlimpton) October 16, 2014