Personal manager Juliet Green told The Associated Press that Shadix had returned to his home state after many years living in Los Angeles.
A cause of death was not immediately known, but his sister, Susan Gagne, told The Birmingham News that he had been using a wheelchair for mobility and appeared to have fallen in his kitchen and struck his head.
A memorial for William G. "Glenn Shadix" Scott will be held Saturday in Birmingham, his website said. Green said he's survived by his mother, sister and brother-in-law.
A biography credits him with over 30 film appearances, and roles in several TV shows, including NBC's "Seinfeld."
"He was one of the most creative, original, funny and wise performers I've ever had the privilege to work with," said Green, who worked with the actor for over a decade.
Green said the prolific actor had one of his closest professional relationships with director Tim Burton, who cast him in films like "The Nightmare Before Christmas," "Planet of the Apes" and "Beetlejuice," the 1988 horror comedy for which he is perhaps most widely remembered.
In the film, Shadix starred opposite Winona Ryder and Michael Keaton as "Otho," an uppity interior designer who tries his hand at the occult to summon ghosts from the afterlife.
In a 2008 interview posted on his website, he said he understood why the film about a recently deceased couple trying to evict a family from its former home became a cult classic.
"There is a part of me that is not surprised," he said. "We had so much fun filming this unusual and so very original movie that I had a feeling something very special was happening."
An official biography says Shadix was born in Bessemer, a suburb of Birmingham, and participated in local theater productions as a youth.
His website also describes him as a photographer and gay rights activist; he spoke publicly about undergoing so-called ex-gay therapy as a teenager.