Some care homes in Wales will be "risk assessed" to determine "whether it is safe" to administer vaccinations there.
On Monday, Welsh ministers set a target to vaccinate all care home residents and staff by the end of January.
Last week, Hywel Dda health board said government guidance stated they should "not administer vaccines in care homes with ongoing cases of Covid-19".
The Welsh Government has now said that isolating those testing positive is an option to enable vaccination.
A spokesperson said rescheduling vaccinations for a later date was another alternative.
Last week, a family from Carmarthenshire told BBC Wales they were facing a "hopeless situation" after their grandfather was denied the Covid-19 vaccine as others in his care home had coronavirus.
Bryn Evans, 87, who lives at Glyn Nest care home in Newcastle Emlyn, was told he could not have the jab until the home went 28 days with no positive cases, despite two negative tests himself.
Hywel Dda health board later confirmed to BBC Wales that it had followed "the current government guidance around vaccination in care home settings which includes not administering vaccines in care homes with ongoing cases of Covid-19".
However, on Monday, Health Minister Vaughan Gething said that all care home staff and residents would be vaccinated by the end of January.
Asked whether this meant a change in guidance from the Welsh Government, a spokesperson said that if residents could be "tested safely" vaccinations could go ahead - if not, vaccinations would be rescheduled.
"Wales' health boards are vaccinating care home residents as a priority," the spokesperson told BBC Wales.
"Clearly, this has to be done safely, and so where a care home has positive cases within the last 28 days the local health board will risk-assess to help determine whether it is safe for residents, staff and vaccinators to enter homes and administer vaccinations.
"Where those testing positive are able to be isolated within the home and residents able to be tested safely, vaccinations may still take place. Alternatively vaccinations will be rescheduled for an agreed date."