Quinn was born in the middle of the Mexican Revolution. His mother, Manuela "Nellie" (née Oaxaca), was a Mexican of Aztec ancestry. His father, Frank "Francisco" Quinn, was born in Mexico to a Mexican mother and an Irish father. Frank fought alongside Pancho Villa.

Years later, he moved to Los Angeles and became an assistant cameraman at a movie studio called Zelig's. In Quinn's autobiography The Original Sin: A Self-Portrait by Anthony Quinn he denied being the son of an "Irish adventurer" and attributed that tale to Hollywood publicists.

When he was six years old, he started attending a Catholic church (for a time thinking that he wanted to become a priest), then later, when he was eleven, joined the Pentecostals in the International Church of the Foursquare Gospel (the Pentecostal followers of Aimee Semple McPherson).

Quinn grew up first in the streets of El Paso, Texas, then later the Boyle Heights and the Echo Park neighborhoods of Los Angeles, California, attending Hammel St. Elementary School, Belvedere Junior High School, and the Polytechnic High School and later Belmont High School. He did not graduate. In the 1990s, Tucson High School in Tucson, Arizona awarded him a high school diploma.

In his youth, Quinn boxed, then studied art and architecture under Frank Lloyd Wright at the latter's Arizona residence and Wisconsin studio, Taliesin, and the two men became friends. When Quinn revealed that he was drawn to acting, Wright encouraged this major change in career direction. In an interview Quinn said that he told Wright that he had been offered $800 a week by a studio and didn't know what to do. Wright told him "Take it, you'll never make that much with me."

After a brief stint in the theater, Quinn launched his film career playing character roles in several 1936 films, including Parole (his debut) and The Milky Way. He mainly played "ethnic" villains in Paramount films through the 1940s in films such as Dangerous to Know (1938) and Road to Morocco.

By 1947, he was a veteran of over 50 films and had played everything from Indians, Mafia dons, Hawaiian chiefs, Filipino freedom-fighters, Chinese guerrillas, and comical Arab sheiks, but he was not a major star. So he made a successful return to the theater, including playing Stanley Kowalski in A Streetcar Named Desire on Broadway.

In 1947, he became a naturalized citizen of the United States. Returning to the screen in the early 1950s, Quinn specialized in tough, macho roles. He was cast in a series of B-adventures like Mask of the Avenger (1951). A big break was his playing opposite Marlon Brando in Elia Kazan's Viva Zapata! (1952). His supporting role as Zapata's brother won Quinn his first Oscar, the first Mexican-American to win any Academy Award.

He appeared in several Italian films starting in 1953, turning in one of his best performances as a dim-witted, thuggish, and volatile strongman in Federico Fellini's La strada (1954), playing alongside Giulietta Masina. Quinn won his second Oscar for Best Supporting Actor for portraying the painter Gauguin in Vincente Minnelli's Van Gogh biopic, Lust for Life (1956).

This award was all the more remarkable given that he was onscreen for all of 8 minutes. The following year, he received yet another Oscar nomination for his part in George Cukor's Wild Is the Wind. In The River's Edge (1957), he played the husband of the former girlfriend (played by Debra Paget) of a killer, played by Ray Milland, who turns up with a stolen fortune and forces Quinn and Paget at gunpoint to guide him safely to Mexico. Quinn starred in The Savage Innocents 1959 (film), in which he starred as Inuk, who finds himself caught between two clashing cultures.

As the decade came to a close, Quinn allowed his age to show, and he began his transformation into a major character actor. His formerly trim physique filled out, his hair grayed, and his once smooth, swarthy face weathered into an appealing series of crags and crinkles. His careworn demeanor made him a convincing Greek resistance fighter in The Guns of Navarone (1961), an ideal ex-boxer in Requiem for a Heavyweight, and a natural for the role of Auda ibu Tayi in Lawrence of Arabia (both 1962).

In that year, he also played the title role in Barabbas, based on the novel by Pär Lagerkvist. The film is an Easter season favorite down to the present day. The success of Zorba the Greek in 1964 was arguably the high water mark of Quinn's career, and resulted in another Oscar nomination. Later successes that decade include La Vingt-cinquième heure (1967; aka The Twenty Fifth Hour), with Virna Lisi; The Magus (1968), with Michael Caine and Candice Bergen, and based on the novel by John Fowles; and The Shoes of the Fisherman, where he played a Russian pope. In 1969, he starred in The Secret of Santa Vittoria with Anna Magnani.

He appeared on Broadway to great acclaim in Becket, as King Henry II to Laurence Olivier's Thomas Becket in 1960. An erroneous story arose in later years that during the run, Quinn and Olivier switched roles and Quinn played Becket to Olivier's King. In fact, Quinn left the production for a film, never having played Becket, and director Peter Glenville suggested a road tour with Olivier as Henry. Olivier happily acceded and Arthur Kennedy took on the role of Becket for the tour and brief return to Broadway.

In 1971, after the success of a TV movie named The City, where Quinn played Albuquerque Mayor Thomas Jefferson Alcala, he starred in the short-lived (1-season) television drama spin-off The Man in the City. His subsequent television appearances were sporadic (among them Jesus of Nazareth).

In 1977, He starred in the movie Mohammad, Messenger of God (aka The Message), about the origin of Islam, as Hamzah, a highly revered warrior instrumental in the early stages of Islam. In 1982, he starred in the Lion of the Desert, together with Irene Papas, Oliver Reed, Rod Steiger, and John Gielgud. Quinn played the real-life Bedouin leader Omar Mukhtar who fought Mussolini's Italian troops in the deserts of Libya.

The film, produced and directed by Moustapha Akkad, is now critically acclaimed, but performed poorly at the box office because of negative publicity in the West at the time of its release, stemming from its having been partially funded by Libya's Muammar al-Gaddafi. In 1983, he reprised his most famous role, playing Zorba the Greek for 362 performances in a successful revival of the Kander and Ebb musical Zorba.

His film career slowed during the 1990s, but Quinn nonetheless continued to work steadily, appearing in Revenge (1990), Jungle Fever (1991), Last Action Hero (1993), and A Walk in the Clouds (1995). In 1994, he played Zeus in the five TV movies that led to the syndicated series Hercules: The Legendary Journeys. (However, he did not continue in the actual series, and the role was eventually filled by several other actors).