The Bad Seeds musician, known for hits such as Into My Arms and One More Time With Feeling, said his son had "passed away".
In a statement, the frontman said: "With much sadness, I can confirm that my son, Jethro, has passed away.
"We would be grateful for family privacy at this time."
Fashion model Jethro had previously been jailed following an assault on his mother Beau Lazenby, and was diagnosed with schizophrenia, according to the Guardian.
It is the second family tragedy for Cave, following the accidental death in 2015 of one of his twin sons Arthur, who was 15.