ARID1A, encoding a subunit of the SWI/SNF chromatin-remodelling complex, is the most frequently mutated epigenetic regulator across all human cancers. ARID1A and TP53 mutations are typically mutually exclusive. Therapeutic approaches that correlate with this genetic characteristic remain to be explored. Here, we show that HDAC6 activity is essential in ARID1A-mutated ovarian cancers. Inhibition of HDAC6 activity using a clinically applicable small-molecule inhibitor significantly improved the survival of mice bearing ARID1A-mutated tumours. This correlated with the suppression of growth and dissemination of ARID1A-mutated, but not wild-type, tumours. The dependence on HDAC6 activity in ARID1A-mutated cells correlated with a direct transcriptional repression of HDAC6 by ARID1A. HDAC6 inhibition selectively promoted apoptosis of ARID1A-mutated cells. HDAC6 directly deacetylates Lys120 of p53, a pro-apoptotic post-translational modification. Thus, ARID1A mutation inactivates the apoptosis-promoting function of p53 by upregulating HDAC6. Together, these results indicate that pharmacological inhibition of HDAC6 is a therapeutic strategy for ARID1A-mutated cancers.