Adelaide Jockey Matthew Neilson has been diagnosed with four fractured vertebrae after falling in a race at Morphettville but has escaped damage to his spinal cord.

Neilson suffered the fractures to his C1, C2, C4 and T5 vertebrae in the fall in the first race on Saturday but he is not expected to need surgery.

A statement from Thoroughbred Racing SA on Sunday said doctors at the Royal Adelaide Hospital expect Neilson to be walking within a few days and to wear a neck brace for four to six weeks.

"Matthew is resting comfortably and he and wife Trish would like to express their sincere appreciation for the many messages of support they have received," the statement said.

His mount Charossa escaped serious injury in the incident.