Coach Sabri Lamouchi confirmed the Hannover forward was also in doubt for their final Group C clash with Greece in Fortaleza on Tuesday.
Ya Konan came on as a second-half substitute in the Ivorians' 2-1 win over Japan but almost immediately looked to be struggling, and Lamouchi confirmed on Thursday that he hopes to put his player on ice with an eye to the knockout stages.
"We do not want to take any risks with him," Lamouchi said, ahead of Ivory Coast's clash with the Colombians in Brasilia.
"We hope he will recover as early as the match against Greece but if that doesn't happen then maybe for the second round."
Lamouchi warned Ivory Coast's inexperience at World Cups could be a factor against the battle-hardened Colombians, and claimed the midfield stoush would be influential to the result.
"Colombia and Ivory Coast have never faced each other in their history," Lamouchi said.
"I want to emphasize first that Ivory Coast will play in only its eighth World Cup match ever, so the game against Colombia...will be totally different opposition to Japan.
"These are two teams with an opposite style. We know it will be a tough match. We will not get that much space.
"It will be a match where we need to win our duels in midfield to impose our game. We know we have the weapons to compete but we must be careful."
Lamouchi was not underestimating Colombia's attacking strength, despite Radamel Falcao absent from their squad to injury and Carlos Bacca ruled out of their clash on Thursday.
"It's a team that has offensive strengths. Just look at their bench," Lamouchi, a former France international, said.
"Jackson Martinez came on during the match against Greece. They have many important assets.
"I don't know how they will approach the game. What I know is that it will be different from the match against Japan.
"We have to be ready to face the Colombians tomorrow."
