Nonsense mutations are involved in multiple peripheral neuropathies. These mutations induce the presence of a premature termination codon (PTC) at the mRNA level. As a result, a dysfunctional or truncated protein is synthesized, or even absent linked to nonsense-mediated mRNA degradation (NMD) system activation. Readthrough molecules or NMD inhibitors could be innovative therapies in these hereditary neuropathies, particularly molecules harboring the dual activity as amlexanox. Charcot–Marie–Tooth (CMT) is the most common inherited pathology of the peripheral nervous system, affecting 1 in 2500 people worldwide. Nonsense mutations in the GDAP1 gene have been associated with a severe form of CMT, prompting us to investigate the effect of readthrough and NMD inhibitor molecules. Although not clearly defined, GDAP1 could be involved in mitochondrial functions, such as mitophagy. We focused on the homozygous c.581C>G (p.Ser194*) mutation inducing CMT2H using patient human induced pluripotent stem cell (hiPSC)-derived neuronal cells. Treatment during 20 h with 100 µM of amlexanox on this cell model stabilized GDAP1 mRNAs carrying UGA-PTC and induced a restoration of the mitochondrial morphology. These results highlight the potential of readthrough molecules associated to NMD inhibitors for the treatment of genetic alterations in CMT, opening the way for future investigations and a potential therapy.