Strettle is in hospital after being hit by the stomach virus that has affected a handful of England players, including Wilkinson.
While Wilkinson has returned to training after spending two days in bed earlier this week, Strettle's tour could be over.
Gloucester back Iain Balshaw will replace him and win his 30th cap, with the bench vacancy caused by his promotion being filled after England train at Vodacom Park, Bloemfontein on Friday.
Wilkinson said: "I am okay. I had a couple of days in bed, and I am coming through the back end of it now. It should be perfect timing - I trained today (Friday).
"I have only really missed one training session, and I am fully fit and healthy."
But Strettle, who shot to prominence during England's RBS 6 Nations campaign earlier this season, has not been so lucky.
England team doctor Simon Kemp said: "David's vomiting continued through yesterday (Thursday), and he was unable to take fluids by mouth.
"He was therefore admitted to a local hospital for rehydration and monitoring, and while he has made good progress, he will not be fit to play on Saturday."
England can now only hope Farrell makes it, and assistant coach Mike Ford added: "Andy is a tough guy. I think he will be there for us on the weekend."
Wilkinson, whose career has been repeatedly stalled by injury setbacks since he kicked England to 2003 World Cup glory, starts his first Test for three months.
There are many who feel he should have been rested from the two-Test South Africa mission - which sees England facing the Springboks without numerous leading players - before far more significant business of World Cup training camps, warm-up games and then the Webb Ellis Trophy defence in France.
But he said: "I have an opportunity to represent my country on a tour to South Africa, so I don't really need any other reason to be here. I am here to try and add whatever I can to the team and the squad.
"On a personal front, I am here to try to better myself, to further my learning which has been a bit stunted over the last three years, and get some experience under pressure against one of the best teams in the world.
"It is a valuable opportunity to learn and learn quickly, which is of the essence with the World Cup just around the corner. It is an ideal place to be, provided we go out there and we perform to our potential."
Wilkinson steered England to a famous victory over the Springboks in Bloemfontein seven years ago, kicking all their points for a 27-22 success, yet he is not into history lessons and also distances himself from talk of South Africa wanting revenge for a 53-3 humiliation at Twickenham in 2002.