Four wards at Glangwili Hospital in Carmarthen have been closed to visitors due to an outbreak of diarrhoea and vomiting.
People are not being allowed on to Cleddau, Padarn, Towy and Dewi wards, and visiting on all other wards is restricted.
Hywel Dda Health Board said that visitors to Withybush Hospital in Haverfordwest are currently restricted to two people per patient.
Updates on loved ones can be provided to family members by telephone.
The health board is also asking members of the public suffering, or who have recently suffered from diarrhoea and vomiting or flu to not visit any hospital or care facility.
A spokesman for the health board said: "Whilst unpleasant, diarrhoea and vomiting is rarely serious and most people make a full recovery within one or two days.
"However, the virus can be more serious for sick and vulnerable patients so if you feel unwell or have nausea or have diarrhoea and vomiting we ask that you wait at least 48 hours after becoming symptom-free before visiting any hospital or care facility.
"If you are experiencing these symptoms it is important to wash and dry your hands thoroughly after going to the toilet and before you handle food to prevent it being passed on to others.
"There is no specific treatment and the general advice is to drink lots of water and take lots of rest."