Calderón died in hospital from natural causes, a family spokesperson confirmed to Deadline.
The star had an acting career spanning six decades and appeared in more than 40 Hollywood films.
However, it was his role in the 2007 movie Pirates of the Caribbean 3: At World’s End for which he remains best known. He appeared as as Captain Villanueva and starred opposite Johnny Depp.
The actor also famously portrayed a character whose head appears on a sword held by an alien in the 1997 movie, Men in Black.
In a recent interview with The Los Angeles Times, the star admitted he cherished taking the role of villainous characters: "I love to play those types of characters, because people really hate me."
He continued: "They tell me in the streets how much they hate me. But to me, that is my success. Because that means I was able to convince people with what I performed."
Talking about how he loves it whenever anyone recognises him for any role, he added: "If I can make them cry and I can make them laugh, then maybe I’m a good actor."
Calderón’s other appearances include The Bridge in the Jungle (1971), Duck, You Sucker! (1971), Under the Volcano (1984), horror film The Ruins (2008) and Pamela Adlon’s series Better Things.
The star also appeared alongside Cate Blanchett in The Missing, as well as alongside Robert De Niro, Barbra Streisand and Ben Stiller in Little Fockers.
Calderón’s most recent roles were as Detective Silverio Narro in The Resort and Carter in The Seven Faces of Jane.
Following the tragic news of his passing, fans have shared tributes on social media, with one writing: "I'm so sad Sergio Calderón has passed. I just read that wonderful article about him in the LA Times too :( I always think of him as El Cajon the river pirate from The A-Team."
The actor is survived by his wife, Karen Dakin; his children, Patrick Calderón-Dakin and Johanna Calderón-Dakin; and his grandchildren, Krishnaavi, Emiliano and Victoria.