Gbagbo was arrested in Abidjan with the help of French peacekeepers in April 2011, ending a long period of political violence that pushed Ivory Coast to the brink of civil war.
The ICC said there are "reasonable grounds" to believe Gbagbo bears criminal responsibility "as an indirect co-perpetrator" on four counts of crimes against humanity, including rape and murder.
The court said three medical experts examined Gbagbo in June to determine if he was fit to stand trial. A confidential medical report was filed in July. The prosecution and defense were called on by the court to submit observations this month.
"In light of the importance of the issue, the (trial) chamber decided to postpone the confirmation of charges hearing until such issue is resolved," an ICC statement read.
Human rights groups believe forces loyal to Ivorian President Alassane Ouattara likely committed atrocities during the conflict.
Renewed concerns about conflict in Ivory Coast have been expressed by the United Nations. A recent attack on a refugee camp was said to be ethnically motivated.