Charcot-Marie-Tooth disease (CMT) is the most common inherited disorder of the peripheral nervous system. Mutations in the 27-kDa small heat-shock protein gene (HSPB1) cause axonal CMT or distal hereditary motor neuropathy (distal HMN). We developed and characterized transgenic mice expressing two different HSPB1 mutations (S135F and P182L) in neurons only. These mice showed all features of CMT or distal HMN dependent on the mutation. Expression of mutant HSPB1 decreased acetylated α-tubulin abundance and induced severe axonal transport deficits. An increase of α-tubulin acetylation induced by pharmacological inhibition of histone deacetylase 6 (HDAC6) corrected the axonal transport defects caused by HSPB1 mutations and rescued the CMT phenotype of symptomatic mutant HSPB1 mice. Our findings demonstrate the pathogenic role of α-tubulin deacetylation in mutant HSPB1-induced neuropathies and offer perspectives for using HDAC6 inhibitors as a therapeutic strategy for hereditary axonopathies.