It was announced last week the 61-year-old would not be returning to the rock band after taking a break earlier this year due to an unspecified illness.
"Malcolm is suffering from dementia and the family thanks you for respecting their privacy," his family told People.
The band are due to release a new album, Rock or Bust, in December and embark on a world tour next year.
The group said last week that "due to the nature of Malcolm's condition" Young would not feature on the new recordings or participate in the tour.
His nephew, Stevie Young, will accompany the band on tour after playing rhythm guitar on the album.
The news confirms rumours that the musician was suffering from the illness.
The Sydney Morning Herald reported Young had been moved into full-time care at a nursing home in Sydney.
According to a family friend, the guitarist could no longer remember how to play AC/DC songs.
"If you were in the room with [Young] and walked out, then came back in one minute later, he wouldn't remember who you are. He has a complete loss of short-term memory," the unnamed source said.
Scottish-born brothers Malcolm and Angus Young formed AC/DC in 1973.
The Australian band have sold more than 200 million albums, with their 1980 record Back in Black their biggest-selling hit.
AC/DC founding member and guitarist Malcolm Young is suffering from dementia, his family has confirmed.