Family spokeswoman Lori De Waal told the Associated Press that the cause of death had not been determined.
Hillerman received four Emmy nominations (and one win) and five Golden Globe nominations (and one win) for his performance as Jonathan Quayle Higgins III, the stuffy sidekick to Tom Selleck's titular private investigator.
Hillerman's career began in local theater. After serving in the Air Force, he moved to New York City to study acting. He soon became a fixture on Broadway before moving on to films including "The Last Picture Show," "Paper Moon," "Blazing Saddles," and "Chinatown."
In 1975, he starred in "Ellery Queen" as snooty radio detective Simon Brimmer, who was a precursor to Higgins. Hillerman also had recurring roles in "One Day at a Time" and "The Betty White Show." He retired from acting in 1999.