Cas13 nucleases are a class of programmable RNA-targeting CRISPR effector proteins that are capable of silencing target gene expression in mammalian cells. Here, we demonstrate that RfxCas13d, a Cas13 ortholog with favorable characteristics to other family members, can be delivered to the mouse spinal cord and brain to silence neurodegeneration-associated genes. Intrathecally delivering an adeno-associated virus vector encoding an RfxCas13d variant programmed to target superoxide dismutase 1 (SOD1), a protein whose mutation can cause amyotrophic lateral sclerosis, reduced SOD1 mRNA and protein in the spinal cord by >50% and improved outcomes in a mouse model of the disorder. We further show that intrastriatally delivering an RfxCas13d variant programmed to target huntingtin (HTT), a protein whose mutation is causative for Huntington’s disease, led to a ~50% reduction in HTT protein in the mouse brain. Our results establish RfxCas13d as a versatile platform for knocking down gene expression in the nervous system.