Team principal Colin Kolles said: "It looks as if Sakon Yamamoto has food poisoning and he doesn't feel well.
"Because of this, Christian Klien will be driving the car this Friday and the rest of the Singapore Grand Prix.
"I hope Sakon gets well soon and is able to drive at his home grand prix in Japan."
Klien has experience of the car, having driven it in Friday practice at two grands prix this season.
He last appeared on the race grid in 2006, his last appearance for Red Bull. He made 46 appearances for that team and its previous incarnation Jaguar.
Since 2006 he has tested for Honda, BMW and Hispania.