Bella the terrier was found with hardly any hair left on her body by an RSPCA inspector last year.
Owners Craig and Sophie Palmer of Llwynhendy admitted causing unnecessary suffering to a dog at a pre-trial hearing in Llanelli on Thursday.
It heard that Bella had made an "incredible transformation" after veterinary treatment.
The district judge banned the couple from keeping animals for three years and sentenced them to 90 hours of unpaid work with 12-month supervision.
They each must also pay £250 costs, and a £60 victim surcharge.
RSPCA inspector Rohan Barker said Bella had been allowed to get "into a truly shocking state" with a serious skin condition.
"This case highlights exactly what can happen if an owner does not ensure their animals receive appropriate veterinary care," he said.
"Fortunately, after getting the treatment she so desperately needs, Bella has undergone an incredible transformation."
A Carmarthenshire couple has been banned from keeping animals after a dog was found in a "shocking state".