The entire South Africa squad are self-isolating after three unnamed players tested positive for Covid-19.
The Springboks cancelled a Sunday training session and a decision on further team activities will be taken shortly, South African Rugby said in a statement.
The Boks are scheduled to go into a bio-secure environment along with the British and Irish Lions, who were leaving for South Africa on Sunday.
South Africa and also due to play two Tests against Georgia on 2 and 9 July, their first since they lifted the Rugby World Cup in November 2019.
The Lions will play eight games on the tour, starting on Saturday against South Africa's Johannesburg-based Lions franchise.
The three Test matches against South Africa will be played on consecutive Saturdays from 24 July.
South Africa is in the grip of a third wave of Covid-19 infections, led by the Delta variant that was first discovered in India.
President Cyril Ramaphosa is scheduled to address the country later on Sunday when he is expected to announce tighter lockdown regulations.