Molina was born Alfredo Molina in London. His father was a Spanish Communist from Madrid who worked as a waiter and chauffeur, while his mother was an Italian housekeeper who also cleaned rooms in a hotel and worked as a cook. Molina grew up in a "working-class neighborhood" in Notting Hill that was inhabited by many other immigrant families. He decided to become an actor after seeing Spartacus at the age of nine, and attended the Guildhall School of Music and Drama.

In 1978, Molina starred with Leonard Rossiter in the sitcom The Losers. Molina made his film debut with a minor role in the 1981 movie Raiders of the Lost Ark as Indiana Jones' ill-fated guide during its iconic opening sequence. However, his big break came with Letter to Brezhnev in 1985, which he followed up with a starring role in Prick Up Your Ears in 1987, playing Joe Orton's lover Kenneth Halliwell. He was given a lead role in the Red Dwarf TV series, but was replaced by another actor.

He starred in the first two series of El C.I.D. but left to concentrate on his film work. Subsequent films included Species, Dudley Do-Right, Chocolat, Not Without My Daughter, and Enchanted April. He has worked twice with Paul Thomas Anderson, first in Boogie Nights and then Magnolia. In 2002, Molina gained wide recognition for his portrayal of Mexican muralist Diego Rivera alongside Salma Hayekin the biopic Frida, a role which garnered him BAFTA and SAG award nominations. In 2003, he played himself alongside Steve Cooganin Coffee and Cigarettes. In 2004, Molina gained further commercial recognition when he was cast as the villain Doctor Octopus in Spider-Man 2, which went on to become one of the highest-grossing films of that year. In 2006, Molina portrayed Touchstone in Kenneth Branagh's film version of Shakespeare's As You Like It and played a lead role in Ron Howard's adaptation of The Da Vinci Code which was also a commercial success that year.

Molina's stage work has included two major Royal National Theatre productions, Tennessee Williams' The Night of the Iguana (as Shannon) and David Mamet's Speed the Plow (as Fox). In his Broadway debut, Molina performed in Yasmina Reza's Tony Award-winning play 'Art', for which he received a Tony nomination in 1998. In 2004, Molina returned to the stage, starring as Tevye in the Broadway production of Fiddler on the Roof. For his performance he once again received a Tony Award nomination, this time for Best Actor in a Musical.

In 2007, Molina narrated a 17-part original audiobook for Audible.com called "The Chopin Manuscript". This serialized novel was written by a team of 15 best-selling thriller writers, including Jeffery Deaver, Lee Child, Joseph Finder and Lisa Scottoline.

Molina has taken U.S. citizenship. He has been married to actress Jill Gascoine since 1985. He has a daughter Rachel (born 1980) from a previous relationship, and two stepsons (Adam and Sean), from Jill's first marriage. He is also a grandfather to Alfie (born Nov 2003) and Layla (born May 2006).