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".