Significance The protein kinase MEKK1 activates stress-signaling pathways in response to various cellular stressors, including chemotherapies that disrupt dynamics of the tubulin cytoskeleton. We show that MEKK1 contains a previously uncharacterized domain that can preferentially bind to the curved tubulin heterodimer—which is found in soluble tubulin and at sites of microtubule assembly and disassembly. Mutations that interfere with MEKK1−tubulin binding disrupt microtubule networks in migrating cells and are enriched in patient-derived tumor sequences. These results suggest that MEKK1−tubulin binding may be relevant to cancer progression, and the efficacy of microtubule-disrupting chemotherapies that require the activity of MEKK1.