The molecular mechanisms discriminating between regenerative failure and success remain elusive. While a regeneration‐competent peripheral nerve injury mounts a regenerative gene expression response in bipolar dorsal root ganglia (DRG) sensory neurons, a regeneration‐incompetent central spinal cord injury does not. This dichotomic response offers a unique opportunity to investigate the fundamental biological mechanisms underpinning regenerative ability. Following a pharmacological screen with small‐molecule inhibitors targeting key epigenetic enzymes in DRG neurons, we identified HDAC3 signalling as a novel candidate brake to axonal regenerative growth. In vivo, we determined that only a regenerative peripheral but not a central spinal injury induces an increase in calcium, which activates protein phosphatase 4 that in turn dephosphorylates HDAC3, thus impairing its activity and enhancing histone acetylation. Bioinformatics analysis of ex vivo H3K9ac ChIPseq and RNAseq from DRG followed by promoter acetylation and protein expression studies implicated HDAC3 in the regulation of multiple regenerative pathways. Finally, genetic or pharmacological HDAC3 inhibition overcame regenerative failure of sensory axons following spinal cord injury. Together, these data indicate that PP4‐dependent HDAC3 dephosphorylation discriminates between axonal regeneration and regenerative failure.