Chelsea's first choice returned to the London club's line-up over the weekend against Newcastle United after being sidelined for two games by a calf injury.
Czech FA spokesman Jaroslav Kolar could not say how long the injury will keep Cech out of action.
"Petr Cech will not play (on Wednesday) because he has a swollen, or maybe even broken upper part of his pinkie finger," Kolar said.
"It is still too early to say how long he will be unable to play. He just went for an examination, so we will give more details likely tomorrow... when we have the doctor's findings."
Jan Lastuvka will replace Cech in goal for the friendly with and Jaroslav Drobny will fill his spot in the squad.
The Czech squad travel to Turkey before facing World Cup qualifying matches at home to Denmark and away against Armenia on March 22 and March 26.
They are third in Group B with five points after three matches, trailing leaders Italy on 10 points and Bulgaria on six points, both of whom have played four matches so far.