The URC pair, along with Scarlets and Zebre, had been looking to return home after South Africa was placed on the Government’s travel red list.
The two United Rugby Championship sides had been hoping to fly out of Cape Town on Sunday after South Africa was added to the UK Government’s travel red list.
URC had been scheduled to stage its first fixtures on South African soil this weekend, but all four games were postponed.
Munster said: “This morning Munster Rugby were making plans to join their fellow URC sides in departing Cape Town for Dublin by charter.
“After arriving at their hotel in Cape Town late last night the squad underwent a round of PCR testing ahead of today’s possible departure. The returning results have identified one positive case.
“In taking all precautions and prioritising the health and wellbeing of everyone Munster Rugby will not travel today and will return to their hotel for an isolation period as a matter of priority. The province will await further guidance from the health authorities.”
The four round-six fixtures – Scarlets v Sharks, Cardiff v Lions, Munster v Bulls and Stormers v Zebre Parma – were called off after UK officials sounded the alarm over a new variant of the virus in South Africa, which has the potential to evade immunity built up by vaccination or prior infection.
Cardiff said they have been unable to depart following two positive cases, one of which is suspected to be the new variant Omicron.
The Welsh club said in a statement: “As a consequence of one of these results suspected of being Omicron, the entire travelling party have returned to their hotel to isolate.
“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.”
Zebre chairman Michele Dalai had earlier tweeted that all four visiting sides would be flying from Cape Town at 12pm and landing in Dublin at 10pm.
Round seven fixtures, scheduled to take place in South Africa next weekend, have also been postponed.