It was not clear if those involved were England players.
“Cricket South Africa (CSA) and the England and Wales Cricket Board (ECB) have agreed to cancel today’s Betway One-Day International series opening match, which was due to take place in Paarl,” the governing bodies said in a statement.
Ashley Giles, the managing director of England Men’s Cricket, said: “We regret that we are unable to play in today’s ODI, but the welfare of the players and support staff is our primary concern and whilst we await the results of further tests the medical advice from both teams was that this game should not take place.
“We remain in constant dialogue with Cricket South Africa and will continue to work closely with them to determine how best to move forward.”
CSA said the England players and management underwent an additional round of tests on Saturday evening after two members of staff at their hotel tested positive for the virus.
Former England captain Mike Atherton, now a commentator and journalist, said he feared the entire series could be under threat.
Atherton said the new positive cases had “ramped up” the concern that the England camp already felt after the opening match was postponed.
“Certainly this match is off and I would be pessimistic about the other games,” said Atherton.