The club confirmed one of the cases is suspected to be the Omicron variant that sparked travel restrictions on flights from South Africa to the UK.
A Cardiff statement said: "PCR tests undertaken last night have returned two positive results."
However, Welsh rivals Scarlets are on the flight both teams were due to take.
Irish side Munster also have a positive Covid case and, like Cardiff, must remain in isolation in South Africa.
Cardiff's playing and coaching staff have "returned to their hotel to isolate".
Their statement added: "Cardiff Rugby continue to work with the South African Rugby Union, the Welsh Rugby Union and public health authorities both at home and abroad to decide the next course of action.
"The club are also continuing to work with all relevant authorities to secure the travelling party's return to Wales when safe and appropriate.
"Everybody concerned in this highly challenging situation would like to thank their families, friends, colleagues and the wider rugby family for their many messages of concern and well wishes.
"No further comments will be made at this time."
South African government guidelines say individuals who test positive for Covid must isolate for 14 days from the day of developing symptoms, not the day of the positive result.
There has been no confirmation that either or both of Cardiff's cases are symptomatic.
Cardiff were in South Africa to play in the United Rugby Championship, but all the tournament games in the country over this and next weekend have been called off.
In the meantime, Cardiff and Scarlets were attempting to return home as soon as possible.
Photo Rugby Planet