The Newport Gwent Dragons scrum-half was originally named on the bench for the Springboks Test but has failed to recover from a bruised knee suffered playing against Newcastle Falcons a fortnight ago.
Llanelli Scarlets' Michael Phillips will take his place among the replacements but Wales coach Mike Ruddock is confident that Cooper will recover soon.
'It's very unfortunate for Gareth because he's been in great form and is highly rated by the entire management team and I'm sure we will see him at some point during the Autumn international series,' said Ruddock. 'Thankfully the injury is not serious and is something that can be worked on but there was no point risking him for this weekend.'
It is the second time this year that Cooper, capped 20 times, has missed out on facing the Springboks after a back problem ruled him out of the summer's tour to Argentina and South Africa.
However, the injury is another opportunity for rising star Phillips to taste international rugby having made twice stepped off the bench during that tour after making his debut against Romania before the World Cup.