The actor was under hospice care when he died Thursday, The Dallas Morning News reported Friday.
Schellenberg was born in Montreal and was of Mohawk and Swiss-German descent, and frequently played American-Indian characters, including Sitting Bull in HBO's 2007 production of "Bury My Heart at Wounded Knee," the newspaper said. That role earned him an Emmy nomination.
Schellenberg began his career as a stage actor, winning the Tyrone Guthrie Award for most promising young actor at the Stratford Festival in Ontario, his son-in-law, Adrian Churchill said.
"He did a lot of stage work at the early part of his career and then in his 40s he started doing a lot more film work," Churchill said. "His first big film -- with a great deal of international success -- was 'Black Robe.'"
The actor appeared on television with roles in "Walker, Texas Ranger," "Grey's Anatomy" and "Saving Grace."
It was his work on "Walker, Texas Ranger" that made him decide to move to Dallas, the Morning News said.
"He liked it here in Texas so much that he decided that this is a great place, halfway between New York and LA," Churchill said.
Schellenberg's final role was in the Canadian film, "The Last Movie," The Hollywood Reporter said.
Schellenberg is survived by wife Joan Karasevich, three daughters and three grandchildren.