The positive for England is that after Saturday’s match against the Proteas they do not play again until a one-off Test against Zimbabwe on 22 May.
Wood is not scheduled to play in the upcoming Indian Premier League or Pakistan Super League.
Captain Ben Stokes is currently out after hamstring surgery but Durham coach Ryan Campbell told BBC Test Match Special on Thursday he expects the all-rounder to play in the County Championship prior to the Zimbabwe Test.
“The stuff he does to get himself ready to play is unbelievable,” said Campbell.
“How are you going to prepare him for the Ashes? The only thing I can say as a given is that nobody will be more prepared than Ben Stokes.”
“He will put himself through hell and back to get ready and be OK.”
Defeat against South Africa would be England’s seventh in a row in one-day internationals and would make it their worst losing run in the format since 2006.
They have also not exited a global event without winning a match since the International Cricket Council Knockout event in 2000. They have never failed to win a match at an ICC event with a group stage.