Duminy - who has been undergoing treatment for a left knee injury suffered in Australia last month - was expected to be fit for the second Test in Port Elizabeth on December 26, over a week after the series gets underway in Centurion on Wednesday.
However, the 30-year-old is facing the likelihood of missing the entire series, according to coach Russell Domingo.
"It's highly unlikely [he'll play in Port Elizabeth]," Domingo said on Saturday.
"The medical committee will hand a report back on that. His treatment is going fine at the moment, but he'll probably take a bit longer than anticipated."
Part of South Africa's reluctance to rush Duminy back from injury is the upcoming Cricket World Cup in Australia and New Zealand, starting in February.
"Guys want to play Test cricket if they're available," Domingo added.
"Also we have to realise the World Cup is just over two months away and JP is a big player for us in that format, as well as every format. We need to assess where he is in the next week or two and then make a decision."
Domingo also leapt to the defence of under-fire opener Alviro Petersen, who has gone 23 Test innings without a century.
"I honestly believe there is a big score around the corner for him, technically he's playing well," he added.
"And he seems to thrive when he has got a point to prove, when people are trying to write him off. I don't think he needs too much motivation.
"I know there a lot of questions about his selection but to me, he has been a good performer for South Africa over a period of time. All players go through slumps."