Hickman's early screen appearance was in the 1942 Our Gang comedy Melodies Old and New. He had small roles in Captain Eddie (1945), The Hoodlum Saint (1946), The Return of Rusty (1946) and Faithful in My Fashion (1946).

In 1946, Hickman played young Chase in the movie The Secret Heart which starred Claudette Colbert, Walter Pidgeon, Lionel Barrymore and June Allyson.

Hickman was in For the Love of Rusty (1947), The Son of Rusty (1947), Heaven Only Knows (1947) (starring Bob Cummings, who would play a major role in Hickman's career), Her Husband's Affairs (1948), My Dog Rusty (1948), Rusty Leads the Way (1948),The Boy with Green Hair (1948), The Sun Comes Up (1949), Rusty Saves a Life (1949), Mighty Joe Young (1949), Rusty's Birthday (1949), and The Happy Years (1950), which starred Darryl. As a teen, he and Darryl guest-starred in a 1950 episode of The Lone Ranger titled Two Gold Lockets,

The usually brown-haired Hickman portrayed Chuck MacDonald, Bob Collins's (played by Bob Cummings) crazy teenaged nephew, on the 1950s NBC series The Bob Cummings Show (a.k.a. Love That Bob in reruns), and the blonde title character in CBS's The Many Loves of Dobie Gillis.

Born in Los Angeles, California, and raised Catholic, Hickman is the younger brother of child actor Darryl Hickman. He graduated from Cathedral High School in 1952 and intended to become a Passionist priest, but ultimately chose not to and attended Loyola University.

Hickman gained wide notice as "Chuck" on The Bob Cummings Show from 1955-59. At the time, he was studying at Loyola. Hickman was one of the first stars to have a breakout character in the series.

In 1958, Hickman was cast as the lead of The Many Loves of Dobie Gillis, which aired on CBS from 1959–63. Although at the show's debut the Dobie character was a teenager in high school, Hickman was then 25 years old.

During the series' run Hickman did the voice for Aladdin in 1001 Arabian Nights (1959). On June 23, 1960, Hickman appeared on NBC's The Ford Show, Starring Tennessee Ernie Ford.

Hickman signed a multi-picture deal with American International Pictures. For that studio he starred in Ski Party (1965) opposite Frankie Avalon; How to Stuff a Wild Bikini (1965) with Funicello; and Dr Goldfoot and the Bikini Machine (1965) with Avalon and Vincent Price. He also made a cameo in Sergeant Deadhead (1965).

Hickman had a support part in the comedy Doctor, You've Got to Be Kidding! (1967) but it would be his last feature film for a while. He starred in the pilot for a series, We'll Take Manhattan, but it was not picked up. Neither was Missy's Men.

Hickman found his Future in entertainment behind the scenes, being involved in production roles. From 1977 to 1988, Hickman served as a programming executive at CBS. He took time out for a cameo in the TV movie High School U.S.A. (1983).

In the late 1980s Hickman turned to directing episodic TV, doing episodes of Duet, Charles in Charge, Open House, Designing Women, Get a Life, Head of the Class, Harry and the Hendersons and Sister, Sister.

Hickman reprised his role of Dobie in the TV movie Bring Me the Head of Dobie Gillis (1988). His autobiography is titled Forever Dobie.

He still occasionally acted, appearing in Murder, She Wrote, and A Night at the Roxbury (1996). He had a semi regular role on the TV series of Clueless

He could be seen in Surviving Gilligan's Island: The Incredibly True Story of the Longest Three Hour Tour in History and Angels with Angles (2005).