The Springboks squad had been isolating after three of their players tested positive for Covid-19.
They say they will "immediately resume" preparations for warm-up games against Georgia after feedback from the Medical Advisory Group of the Lions tour.
The Lions tour will start on 24 July with the sides playing three Test matches.
Scrum-half Herschel Jantjies, prop Vincent Koch and wing S'bu Nkosi were named as the three players who had tested positive.
"Three players tested positive for Covid-19 on Sunday following real-time polymerase chain reaction (PCR) tests on arrival at the team hotel in Johannesburg. However, Herschel Jantjies has subsequently been cleared and can return to training," said a statement from South Africa rugby.
"In light of this, as well as the strict precautionary measures taken by the team and the effective isolation protocols since the squad assembled, the Springboks can resume their training programme from Monday afternoon."
The Springboks are scheduled to play the first of two Tests against Georgia on 2 July - their first outing since winning the World Cup in November 2019.