Worthington, 67, had a playing career spanning 26 years that included more than 200 appearances for Leicester.
He started his career at Huddersfield and also played for the likes of Leeds, Bolton Wanderers and Sunderland.
“He was diagnosed several years ago and has been holding it off with positive thinking and football,” wrote Kim-Malou Worthington in a post on Facebook.
“They say several footballers from my dad’s era seem to have suffered the same disease, possibly due to the constant heading of the heavy football back in the day.”
Jeff Astle, another former England striker, died in 2002 from brain trauma which a coroner ruled was caused by heading heavy leather balls.
Three members of England’s 1966 World Cup-winning squad – Martin Peters, Nobby Stiles and Ray Wilson – also have Alzheimer’s, the most common cause of dementia.
The Football Association wants world governing body Fifa to investigate whether former players have dementia as a consequence of playing the game.