"He is critically ill," George Hector told Reuters from Cape Town. "He was admitted to hospital on Monday last week (May 14) for serious but routine surgery, but complications set in afterwards and he has deteriorated since then."
Hector said the family "preferred to keep the details private".
"He is heavily sedated at the moment and unable to communicate," he added.
Sonn, 57, became ICC president in 2006,
He rose through the ranks of the United Cricket Board (UCB), which was formed after the sport unified across racial lines in 1991, and was UCB president from 2000 to 2003.
Sonn, a senior counsel who has been an acting judge, formed and headed the Directorate of Special Operations in South Africa, a crack investigative police unit modelled on the Federal Bureau of Investigation in the United States.