According to his spokesman George Hector, Sonn, 57, was admitted to a high care unit of the Durbanville Medi-Clinic on Monday after suffering complications from a minor colon operation.
"Mr Sonn is critically ill at the moment at the Durbanville Hospital," Hector told AFP.
"He went for a routine surgery last week Monday and developed some complications. He was taken to intensive care and has been there since."
Hector said Sonn's appointment with the doctor had been scheduled "several months" prior to the recent World Cup, where he did not stay for long due to his ill-health.
His wife Sandra and their three children were at his bedside in hospital and no visitors, including the media were allowed, Hector said.
Sonn became ICC president in June 2006 after successfully heading the United Cricket Board of South Africa where he played an integral part in the integration of South Africa into the world game after the end of apartheid.
He was the first African to become head of world cricket's administration. ICC spokesman Brian Murgatroyd said in a statement Tuesday that the news of Sonn's hospitalisation was "extremely upsetting for everyone".
"Everyone was with him at the World Cup where he was his usual jolly self, and to hear this less than a month later is very troubling," Murgatroyd said.