Hillerman's rep confirmed the news on social media but revealed that a cause of death has not been determined.
The actor starred in the long-running 1980s detective show Magnum, P.I. as Jonathan Quayle Higgins III alongside Tom Selleck.
He won an Emmy for best supporting role in 1987 and a Golden Globe in 1982.
Hillerman also starred in a number of films including Blazing Saddles and High Plains Drifter, and had a recurring role on The Betty White Show.