Temporary changes are being made at the Prince Philip Hospital in Llanelli as "a small number of" staff and patients have tested positive for coronavirus.
The positive cases span across two areas - both of which will no longer be accepting new patients for the time being.
Hywel Dda University Health Board said "there are less than 15 individuals between the two areas" who have tested positive.
Several other hospitals across Wales, including three under the Cwm Taf Morgannwg University Health Board, are experiencing Covid-19 outbreaks.
The stroke rehabilitation ward (Ward 9) and the older adult mental health ward (Bryngolau) at the Prince Philip Hospital are temporarily closed to new admissions in response to the positive cases.
The health board said that all patients in those areas "have been tested and are being cared for appropriately".
It added: "Affected staff are also being tested, with appropriate staffing arrangements in place, including stringent infection prevention and control measures and appropriate use of Personal Protective Equipment."
The hospital are still accepting stroke patients but through the Acute Stroke Unit instead, they are also providing alternative care for older adult mental health.
Hospital Director and Respiratory Consultant, Dr Robin Ghosal said: “Covid-19 is circulating in our communities, but thanks to testing and tracing, and stringent infection prevention measures, we are much more aware and able to deal with risks in order to protect our patients, staff and wider community.
“This is why we have contained two areas of Prince Philip Hospital at present. The two situations are not interlinked and we are closely monitoring the situation and working with partners including Public Health Wales and the local authority.
“It is clear that Covid-19 cases are rising in our area and we would like to take this opportunity to ask everyone to follow the guidelines that are in place to protect us all."
It comes as services that were temporarily suspended at the Royal Glamorgan Hospital have started to resume. The health board have been managing a coronavirus outbreak there since late September.