The pioneering group dispelled speculation that they would disband after Young, 61, took his leave, saying "the band will continue to make music."
"Malcolm would like to thank the group's diehard legions of fans worldwide for their never-ending love and support," the group said in a statement.
The band did not say what sort of illness Young was suffering from or whether it would cease from touring without one of its founding members.
The Scotland-born Young founded AC/DC with his younger brother, Angus, in 1973. The band has withstood the loss of a key member in the past, in particular when lead singer Bon Scott died in 1980.
Their 1980 album "Back in Black" is one of the top-selling albums of all time, with more than 20 million in U.S. sales alone. AC/DC most recently completed a 20-month world tour in 2010 in support of their 2008 album "Black Ice."