Oosthuizen was traveling from Mauritius to Johannesburg earlier this week when during the trip he jammed the fingers on his left hand between two airport luggage trolleys.
He withdrew from the final European Tour event of 2017 on Wednesday.
"I didn't play as many tournaments as I usually do a year ago, with family issues", he said.
"I was really looking forward to playing this week". South African Darren Fichardt is the defending champ. He is now backing last week's victor in Mauritius, Frittelli, as the man to beat around the Firethorn and Bushwillow courses at the Randpark club.
Oosthuizen had hoped the injury would recover to tee it up at the tri-sanctioned event, but had to step aside due to being unable to grip his clubs and still being in severe pain.
"I was so pleased when the pro-am on Tuesday was cancelled (because of heavy rain across Joburg) as I was able to get some rest, but the bad thing is the fingers were worse this morning. I tried to grip a golf club but there's no way I can go to my grip position", Oosthuizen said.
"I don't want to tee off Thursday and play one hole or a few shots and then withdraw after taking someone's spot, I just can't do that. I'll be surprised if a South African doesn't win the tournament and having played with Dylan in Mauritius last weekend, he's definitely one of the favourites", Oosthuizen said.
Cody Martin of the USA has been drafted into Oosthuizen's three-ball, which also includes last week's victor in Mauritius, Frittelli, and Jazz Janewattananond of Thailand.