Renshaw stood separately from team-mates during the anthems after reporting feeling unwell and was then seen sat away from the dugout on the boundary edge.
"Australian batter Matthew Renshaw reported feeling unwell shortly before play in the third Test match against South Africa in Sydney and was separated from the squad. Renshaw has since returned a positive RAT test. He will continue to take part in the match," a CA spokesperson said.
On the eve of the Test, Pat Cummins had spoken about how it had been a much more normal summer after two years of various restrictions. "I still don't know how we haven't had Covid in our team yet now I think about," he said.
Renshaw is playing his first Test since 2018 having been listed to bat at No. 6 in Sydney with Australia opting against five specialist bowlers for the final Test.
Instead they have fielded just two frontline quicks, Cummins and Josh Hazlewood, alongside two spinners in the recalled Ashton Agar and Nathan Lyon.
During the 2018-19 series against Pakistan in the UAE, Renshaw had been in line for a place in the team before suffering a concussion in the warm-up match.