The band were forced to cancel a string of shows last year because of Smith's health.
His partner, Pam Van Damned, who also manages the band, said Smith "passed this morning at home", and that the family requested "privacy at this sad time".
Born in Salford in March 1957, Smith wrote music in his lunch breaks while working on the Manchester docks as a shipping clerk.
After attending a Sex Pistols gig in 1976, he quit the docks for The Fall.
Over the next four decades he is said to have hired and fired dozens of musicians.