Background Chemoresistance is associated with recurrence and metastasis in oral squamous cell carcinoma (OSCC). The cancer stem cell (CSC) subpopulation is highly resistant to therapy, and they are regulated by epigenetic mechanisms. HDACs are histone deacetylase enzymes that epigenetically regulate gene expression. HDAC6 acts on several physiological processes, including oxidative stress, autophagy and DNA damage response, and its accumulation is associated with cancer. Here, we investigate the role of HDAC6 in CSC‐mediated chemoresistance in oral carcinoma in addition to its application as a therapeutic target to reverse chemoresistance. Methods Wild‐type oral carcinoma cell lines (CAL27 WT and SCC9 WT), cisplatin‐resistant (CAL27 CisR and SCC9 CisR), and the subpopulations of cancer stem cells (CSC+) and non‐stem (CSC−) derived from CisR cells were investigated. HDAC6 accumulation was analyzed by Western blot and immunofluorescence; DNA damage was evaluated by immunofluorescence of phospho‐H2A.X; the qPCR for PRDX2, PRDX6, SOD2, and TXN and ROS assay assessed oxidative stress. Apoptosis and CSC accumulation were investigated by flow cytometry. Results We identified the accumulation of HDAC6 in CisR cell lines and CSC. Cisplatin‐resistant cell lines and CSC demonstrated a reduction in DNA damage and ROS and elevated expression of PRDX2. The administration of tubastatin A (a specific HDAC6 inhibitor) increased oxidative stress and DNA damage and decreased PRDX2. Tubastatin A as a monotherapy induced apoptosis in CisR and CSC and reduced the stemness phenotype. Conclusion High levels of HDAC6 sustain CSC subpopulation and chemoresistance in OSCC, suggesting HDAC6 as a pharmacological target to overcome resistance and perhaps prevent recurrence in OSCC.