Muraoka was born in Mission Hills, California in 1962. His first experience as a performer came at the age of ten in an elementary school production, where he appeared as "The Candy Man." He continued to perform in school productions through high school. It was also high school that provided Muraoka with his first experience as a director: a highly praised production of Who's Afraid of Virginia Woolf.
In 1980, he was accepted into the Theatre Department of UCLA, where he studied musical theatre. During this time UCLA presented Muraoka with the Carol Burnett Musical Theatre Award for performance. While at college, he also gained experience as a performer in various Walt Disney World productions, during sabbaticals and summer breaks.
After receiving his B.A. in Theatre Arts from UCLA in 1985, Muraoka spent time as a performer on Princess Cruises. He worked for the company for a year and a half before receiving his first Broadway credit, performing six roles in the short-lived production of Mail. After Mail opened (and closed, after one month) in 1988, Muraoka remained in New York.
For the next ten years, Muraoka continued to act in theatrical productions, both on Broadway and in regional and touring productions. Notably, he was a member of the original cast of Shogun: The Musical on Broadway and had a long run in the lead role of "The Engineer" in Miss Saigon. He also appeared in the 1996 revival of The King and I, with Jenna Ushkowitz and Lou Diamond Phillips.
After auditioning several times through 1997, Muraoka joined the cast of Sesame Street in 1998. (He had previously appeared in Sesame Workshop's Square One TV as a stereotypical Japanese chef preparing popovers in a segment about measuring.) While appearing in Sesame Street, Muraoka has continued to perform in theater, earning good reviews in the 2004 Broadway revival of Pacific Overtures and briefly filling in as Iago in Aladdin in 2016.
Following his high school experience as a director, Muraoka's professional directing career got its start on Sesame Street for a yoga class film that appeared in Episode 4180. He was highly praised by the New York Times for his a non-traditional (all-Asian) version of Falsettoland for the National Asian American Theater Company in 1998. In 2004, he directed veteran Sesame Street puppeteers John Tartaglia, Stephanie D'Abruzzo, and Jennifer Barnhart in Empty Handed and John Tartaglia AD-LIBerty. He also directed Ann Harada (star of Avenue Q) in her own one-woman show. He choreographed the Sesame Street float performances in the 2001, 2013, 2014 and 2015 Macy's Thanksgiving Day Parade. He has also directed elements for the rebooted "Elmo's World" segments and "Cookie Monster's Foodie Truck."