Hogg suffered a hamstring injury during the game and, while he is expected to be fit, Scotland are taking no chances with the squad.
Beattie has pulled out of the Under-21 side due to take part in the world championships in France.
But the Scotland boss believes the 20-year-old could still play his part for both teams.
Hadden said: "Ally is making progress. We feel, however, that it makes sense to take some cover with us.
"It's a very tough decision with regards to the Scotland Under-21 team who are leaving today for their world championship in France.
"But we hope events mean that John will still be able to play some part in that tournament.
"In any event, John's involvement on the South African tour is a fantastic development opportunity for him."
The Glasgow player, who is the son of former Scotland and British & Irish Lions number eight John, is also hoping his call-up will still offer the chance of representing his country at both levels.
Beattie said: "It's a win-win situation for me.
"Being called up as cover for South Africa is going to be an awesome experience and, all being well with injuries, it'll be fantastic if I can finish off with the Under-21s given that I've been playing with many of the guys in the squad since I was 17."