Frenchman Gerard Gili, who has led Ivory Coast's under-23 team to the 2008 Olympic finals, will take over the Elephants.
Stielike told the German sports press agency SID that his son was taken into intensive care on Sunday and was in a coma. The former West German national team star said he would definitely miss Ivory Coast's first two games against Nigeria and Benin.
"Everything beyond that depends on my son's condition," Stielike said.
Gili, the former Marseille coach, was the Ivory Coast assistant under Henri Michel in 2006 when the Elephants finished second at the African Nations Cup and played in the World Cup finals in Germany.