The World Cup-winning playmaker injured a calf muscle when playing for his English club Leicester in the Premiership semifinals.
South Africa's director of rugby, Rassie Erasmus, told a press conference this week that it was decided not to rush Pollard's return to play, especially with the Rugby World Cup starting in September.
"Injury-wise, our only real concern is Handre Pollard. That is why we have Elton [Jantjies] here. We don't want to put pressure on guys to play before they are 100 per cent. There is no need. There is a bigger picture, and we have quality depth.
"Handre is a bit of a worry. It's a tricky situation because it's a calf injury that he's re-injured. A re-injury always has us a bit more nervous."
He said concern over Pollard's likely replacement Damian Willemse, who took a blow to his knee during training, had eased and should be ready for the Springboks' opening Rugby Championship game against Australia in Pretoria. The team for that game will be named next Wednesday.
Erasmus said lock Eben Etzebeth was recovering from a shoulder injury while captain, and flanker, Siya Kolisi was also shaping well in getting over his knee injury.
"Those guys we are looking at playing in the [warm-up] game against Wales [on August 19].
The Springboks will also name their squad to travel to New Zealand at the same time as the Wallabies announcement.
Coach Jacques Nienaber said: "We have to get the balance right between having all the guys here in Pretoria to ensure the team to play at Loftus gets the best possible preparation and then getting the other squad to New Zealand in time so that they get over the jet lag.
"We will announce the squad as late as possible because we don't want the opposition to know who they must prepare for."