The actor died in California on Monday night, TMZ reports.
Further details about Bain's death have reportedly not yet been determined.
Bain's daughter Jennifer described her father as an "amazing person" and compared him to his Diff'rent Strokes character Philip Drummond.
"He was a lot like Mr Drummond, but much more interesting in real life," she said, explaining that he spent his last few days with family. "He was an amazing father."
Bain - who is survived by his twin brother, three sons and Jennifer - is also known for his roles in television series such as Maude and Mr President.