Following the discovery of the trio of cases during PCR testing in Johannesburg, the reigning world champions announced the cancellation of a planned training session on Sunday.
Team management will consult with medical experts before deciding what steps to take next, with the isolation of players and staff coming just as the Lions prepare to fly out from Edinburgh.
"The Springboks cancelled Sunday's planned training session in Johannesburg as a precautionary measure when scheduled testing protocols returned three positive COVID-19 test results when the team assembled on Saturday," a statement read.
"Three players tested positive for the virus following stringent real-time polymerase chain reaction (PCR) testing procedures on arrival at the team base.
"Team management immediately put the squad into self-isolation as a precaution until specialist medical advice is sought from the medical advisory group (MAG).
"A decision on further team activities will be made shortly.
"Director of rugby Rassie Erasmus emphasised that the team had followed all the necessary precautions since the start of the three-week conditioning camp hosted in Bloemfontein, which included mandatory COVID-19 testing three times a week, and that they would be led by specialist advice before any action is taken."
The Lions have had problems to deal with before departing for South Africa, captain Alun Wyn Jones suffering a dislocated shoulder during the warm-up win over Japan on Saturday that will see him miss the entire trip.
Fellow Wales international Justin Tipuric is another to be ruled out following the 28-10 victory at Murrayfield, with head coach Warren Gatland calling up Adam Beard and Josh Navidi as replacements.
Conor Murray, meanwhile, is to take over the captaincy duties in the absence of Jones, who was set to lead the squad on his fourth tour with the Lions.
The three-match Test series against the Springboks begins at Cape Town Stadium on 25 July.