Sheen was born in Dayton, Ohio, on August 3, 1940, to Mary-Ann (née Phelan) and Francisco Estévez Martínez. During birth, Sheen's left arm was crushed by forceps, giving him limited lateral movement of that arm (Erb's palsy) and resulting in the arm being three inches (7.6 cm) shorter than his right. Both of Sheen's parents were immigrants; his mother was Irish, from Borrisokane, County Tipperary, and his father, who was Spanish, was born in Salceda de Caselas, Galicia. After moving to Dayton in the 1930s, his father was a factory worker/machinery inspector at the National Cash Register Company. Sheen grew up on Brown Street in the South Park neighborhood, the seventh of ten children (nine boys and a girl). Due to his father's work, the family lived on the island of Bermuda on St. John's Road, Pembroke Parish, where five of his brothers were born. Martin was the first child to be born in Dayton, Ohio, after the family returned from Bermuda. Sheen contracted polio as a child and had to remain bedridden for a year. His doctor's treatment using Sister Kenny's method helped him regain use of his legs.When he was eleven years old, Sheen's mother died, and the children faced the possibility of living in an orphanage or foster homes. The family was able to remain together with the assistance of the Holy Trinity Catholic Church in Dayton. Raised as a Catholic, he graduated from Chaminade High School (now Chaminade Julienne Catholic High School). At fourteen years old he organized a strike of golf caddies while working at a private golf club in Dayton, Ohio. He complained about the golfers, saying: "They often used obscene language in front of us... we were little boys and they were abusive... anti-Semitic.... And they, for the most part, were upstanding members of the community."Sheen was drawn to acting at a young age, but his father disapproved of his interest in the field. Despite his father's opposition, Sheen borrowed money from a Catholic priest and moved to New York City in his early twenties, hoping to make it as an actor. He spent two years in the Living Theatre company. It was in New York that he met Catholic activist Dorothy Day. Working with her Catholic Worker Movement, he began his commitment to social justice, and would one day go on to play Peter Maurin, cofounder of the Catholic Worker Movement, in Entertaining Angels: The Dorothy Day Story. Sheen deliberately failed the entrance examination for the University of Dayton so that he could pursue his acting career.
He adopted his stage name, Martin Sheen, from a combination of the CBS casting director, Robert Dale Martin, who gave him his first big break, and the Catholic televangelist archbishop, Fulton J. Sheen. In a 2003 Inside the Actors Studio interview, Sheen explained, Whenever I would call for an appointment, whether it was a job or an apartment, and I would give my name, there was always that hesitation and when I'd get there, it was always gone. So I thought, I got enough problems trying to get an acting job, so I invented Martin Sheen. It's still Estevez officially. I never changed it officially. I never will. It's on my driver's license and passport and everything. I started using Sheen, I thought I'd give it a try, and before I knew it, I started making a living with it and then it was too late. In fact, one of my great regrets is that I didn't keep my name as it was given to me. I knew it bothered my dad.