Irish sports minister Jack Chambers says Munster have been cleared by South African authorities to return home.
The player that tested positive on Sunday, and one close contact, must remain in South Africa until the end of their isolation period.
All members of the travelling party will be required to quarantine for 10 days upon their return to Ireland.
Munster's plan to leave Cape Town on Sunday was delayed after the positive test was returned.
"The South African health authorities have given approval for the rest of the Munster panel and wider squad to return home, so there is active work ongoing now to allow Munster to get home," minister Chambers told RTE.
"There is intensive work ongoing at the moment to get them home as quickly as possible but, as you know, there are difficulties in the travel situation in southern Africa at the moment."
Munster are next due to play on 12 December when they are set to meet Wasps away in their European Champions Cup opener.
Returning internationals who did not travel with the squad to South Africa following their involvement in Ireland's autumn Tests continue to train back in Limerick.
Munster were set to to face the Bulls on Saturday, but that game was postponed following the detection of the Omicron variant in southern Africa.
The squad will have another round of PCR testing in Cape Town on Monday, with the player who already tested positive isolating in a different hotel.
Welsh side Cardiff remain in Cape Town after two positive cases in their squad were discovered on Sunday, while Scarlets are isolating in a hotel in Belfast having flown into Dublin in the early hours of Monday morning.