Mutations in the small heat shock protein HSPB1 (HSP27) are causative for Charcot-Marie-Tooth (CMT) neuropathy. We previously showed that a subset of these mutations displays higher chaperone activity and enhanced affinity to client proteins. We hypothesized that this excessive binding property might cause the HSPB1 mutant proteins to disturb the function of proteins essential for the maintenance or survival of peripheral neurons. In the present work, we explored this hypothesis further and compared the protein complexes formed by wild-type and mutant HSPB1. Tubulin came out as the most striking differential interacting protein, with hyperactive mutants binding more strongly to both tubulin and microtubules. This anomalous binding leads to a stabilization of the microtubule network in a microtubule-associated protein-like manner as reflected by resistance to cold depolymerization, faster network recovery after nocodazole treatment, and decreased rescue and catastrophe rates of individual microtubules. In a transgenic mouse model for mutant HSPB1 that recapitulates all features of CMT, we could confirm the enhanced interaction of mutant HSPB1 with tubulin. Increased stability of the microtubule network was also clear in neurons isolated from these mice. Since neuronal cells are particularly vulnerable to disturbances in microtubule dynamics, this mechanism might explain the neuron-specific CMT phenotype caused by HSPB1 mutations.