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.

Up to eight people are believed to have carried out the ram-raid at Martins newsagent in Prentice Place, Harlow, at about 01:45 BST.
The ATM was removed from an outside wall, causing "substantial damage", and was then loaded on to a van.
Essex Police are investigating whether the raid is linked to another at a Roydon newsagent earlier this month.
The cash machine contained a "five-figure sum", police said.
It is thought the thieves left in the van and a red car, believed to be an Audi. The digger, which was damaged in the raid, was left at the scene.
"We are especially keen to hear from anyone who saw the JCB, which is not the usual sort of vehicle to be seen on public roads late at night," Det Insp Jim Adams said.
"There was a previous incident involving the theft of a cash machine at a newsagent in Roydon on 16 September in which the machine and its contents were later recovered, and we are looking into whether these two incidents may be linked."
A motorcyclist is in a critical condition in hospital after hitting a sheep in Carmarthenshire.
[NEXT_CONCEPT]
Thieves used a stolen JCB digger to smash into an Essex newsagent and steal a cash machine.