Hickman was born in Hollywood, California to Milton and Katherine Hickman. His father sold insurance and his mother was a housewife. In the mid-1930s, Darryl was discovered by a dance school Director and subsequently became a student there. The following year, the famed Hollywood studio Paramount signed a contract with the child actor. His first film role was as Ronald Colman's son in The Prisoner of Zenda in 1937. He attended Paramount's school in California and had classmates like Gene Nelson and Jackie Cooper.

In preparation for the 1939 Bing Crosby movie The Star Maker, Paramount casting agents, led by Leroy Prinz, interviewed over 1000 children. Hickman won one of the parts in the film. Pleased with Hickman's performance, Crosby notified his older brother and talent agent Everett Crosby of the young actor. After this, he went on to appear in multiple motion pictures throughout the 1930s and 1940s in a wide array of genres. A busy performer, he would sometimes work at different films simultaneously.

In 1940, he was cast in 20th Century Fox's film adaption of John Steinbeck's best-selling novel from 1939 The Grapes of Wrath, starring Henry Fonda and directed by John Ford. He portrayed the role of "Winfield Joad", the youngest member of a family trying to cope with the hardships of The Great Depression. The film was a critical and commercial success, with Ford winning an Academy Award for Best Director, while Actress Jane Darwell won for Best Supporting Actress. Another notable role during this time included the war-time melodrama The Human Comedy, where he played a mentally slow child. Hickman made a featured appearance as well as "Frank" in the 1942 Our Gang comedy short Going to Press.

In 1946, he played the younger version of Van Heflin's character 'Sam Masterson' in the film noir The Strange Love of Martha Ivers. In order to make it seem credible that Hickman looked like a young Van Heflin, the latter provided a picture of himself as a teenager to the makeup Artist Wally Westmore. In this period he also acted alongside Gene Tierney and Cornel Wilde in the 1946 film Leave Her to Heaven. Being the sole survivor among the cast, he provided extra commentary in the DVD release of the movie. His experience of working with Tierney was mixed, considering her to have been aloof and not given her best performance. It won Tierney an Academy Award nomination for Best Actress. The year after the release of Leave Her to Heaven, Hickman was lauded by a newspaper as "one of Hollywood's top juveniles". Hickman later became critical of child acting, lamenting how the profession for young actors deprives them of a real childhood. He opted to get therapeutical assistance for several years in order to come to terms with his past.

Hickman graduated from Cathedral High School in Los Angeles in 1948 (his brother Dwayne graduated from the same school in 1952). Finding it hard to adjust to adulthood after being in the limelight for most of his childhood, he retired from show Business to enter a monastery in 1951 as a passionist monk. He returned to Hollywood around one month later. He continued acting, but with fewer roles than he had at the peak of his career. He also began acting for the first time in the then-new entertainment medium of television. The switch did not always turn out successfully, for many shows were cancelled for various reasons in the early years of television. Hickman's ongoing efforts to reinvigorate his acting career were interrupted for two years while he served in the United States Army from 1954 to 1956.

Hickman married Actress Pamela Lincoln, with whom he had acted in the movie The Tingler, on November 28, 1959. The couple, who had two sons, divorced in 1982. Their younger son, Justin, committed suicide at the age of 19 in 1985.

Hickman eventually became a television executive, Producer, and occasional Screenwriter, mainly working in New York City. He wrote the scripts for several 1961 episodes of The Loretta Young Show. In the early 1970s, Hickman was associate Producer of the long-running Love of Life. He was also one of the producers of A Year at the Top with Norman Lear in 1977. During the production of the pilot episode for A Year at the Top, he reunited with guest-star Mickey Rooney with whom he had acted in the Boys Town sequel Men of Boys Town in 1941.

Hickman's book about acting techniques The Unconscious Actor: Out of Control, In Full Command was published in April 2007. In it he explains how his approach to acting evolved through his interactions with the various actors and Directors he worked with over the years. Among his most important influences came from working with Spencer Tracy and George Cukor in the 1942 movie Keeper of the Flame. In another book written by James Curtis and published in 2011, Spencer Tracy: A Biography, Hickman's admiration for Tracy and Cukor is again documented. He praises the two men's patience in that biography, as well as their ability to give due attention to inexperienced actors such as himself. Earlier, in a 2002 interview, Hickman stated that the current generation of young Hollywood actors were talented but lacked the proper coaching and ambition.