The 45-year-old man from the Swansea valley was riding a Kawasaki ZX 1000 when he crashed into the animal on the A4069 between Llangadog and Brynamman.
He was taken to Cardiff's University Hospital of Wales after the crash, which happened just before 18:00 BST on Sunday.
Dyfed-Powys Police is investigating.
A motorcyclist is in a critical condition in hospital after hitting a sheep in Carmarthenshire.