New signing Pienaar is likely to be out for a fortnight after picking up an injury in a training-ground accident. The South African joins Luka Modric on the sidelines after he was operated on to remove his appendix.
King, meanwhile, suffered the embarrassment of having to cancel his trip to Germany for hernia surgery after failing to find his passport.
"It's a long story," Redknapp said. "Ledley should have had an operation today but he couldn't make it. He couldn't find his passport so he couldn't fly out to get it done.
"The operation was meant to take place in Germany but won't happen until next week now."