However, the reigning champions expect to have lock Eben Etzebeth available for Saturday evening's Pool B fixture at Stade de France.
Pollard was left out of the Springboks' initial 33-man squad for the tournament due to a calf problem before being called up on Sunday in place of injured hooker Malcolm Marx.
The 29-year-old - a key man in his country's victorious 2019 World Cup campaign - returned from injury on Friday evening as a second-half replacement in Leicester's 18-14 Premiership win at Sale.
South Africa's director of rugby Rassie Erasmus said: "He will definitely not be selected for this, apart from if we get two or three injuries.
"He's only just joined us today, he's just played his first minutes in 14, 15 weeks for Leicester on Friday.
"That was basically the initial reason why we couldn't bring him to the World Cup.
"It's good to have him here and now he must get up to speed with our intensity of training sessions, get through our training sessions and slot in nicely.
"We've only played two games in this World Cup so I'm pretty sure somewhere we will press on his button and use him but not this weekend."
Influential lock Etzebeth was forced off by a shoulder injury against the Scots last Sunday but has made a swift recovery.
"He reacted well last week with his return to training, so yes he will be in contention for this week," forwards coach Deon Davids said of the 31-year-old.
South Africa boss Erasmus has been linked with replacing outgoing Irish Rugby Football Union performance director David Nucifora after the World Cup.
However, the 50-year-old dismissed reports he will follow Springboks head coach Jacques Nienaber, who is set to replace Stuart Lancaster in Leinster's coaching staff, to Dublin.
"No, I won't be, there's been no talks (with the IRFU) and there's no truth in that," said Erasmus.
"I'm not sure where it started, but I haven't chatted to them and I'm definitely not following Jacques."