In a video posted online by the jihadists, the Croatian, who was working for a French company, appears kneeling at the feet of a hooded man holding a knife.
He reads from a sheet of paper that he will be executed within 48 hours if the Egyptian government fails to release Muslim women held in prisons.
He did not say from when the countdown began.
The hostage said he was abducted on July 22 by the Sinai Province group, IS's Egyptian affiliate.
The Croatian foreign ministry said the man was kidnapped as he travelled to work in his car.
"The armed group stopped his car, forced the driver out and drove away in an unknown direction," the ministry said at that time, without elaborating.