Small cell carcinoma of the ovary, hypercalcaemic type (SCCOHT) is a rare but aggressive and untreatable malignancy affecting young women. We and others recently discovered that SMARCA4, a gene encoding the ATPase of the SWI/SNF chromatin‐remodelling complex, is the only gene recurrently mutated in the majority of SCCOHT. The low somatic complexity of SCCOHT genomes and the prominent role of the SWI/SNF chromatin‐remodelling complex in transcriptional control of genes suggest that SCCOHT cells may rely on epigenetic rewiring for oncogenic transformation. Herein, we report that approximately 80% (19/24) of SCCOHT tumour samples have strong expression of the histone methyltransferase EZH2 by immunohistochemistry, with the rest expressing variable amounts of EZH2. Re‐expression of SMARCA4 suppressed the expression of EZH2 in SCCOHT cells. In comparison to other ovarian cell lines, SCCOHT cells displayed hypersensitivity to EZH2 shRNAs and two selective EZH2 inhibitors, GSK126 and EPZ‐6438. EZH2 inhibitors induced cell cycle arrest, apoptosis, and cell differentiation in SCCOHT cells, along with the induction of genes involved in cell cycle regulation, apoptosis, and neuron‐like differentiation. EZH2 inhibitors suppressed tumour growth and improved the survival of mice bearing SCCOHT xenografts. Therefore, our data suggest that loss of SMARCA4 creates a dependency on the catalytic activity of EZH2 in SCCOHT cells and that pharmacological inhibition of EZH2 is a promising therapeutic strategy for treating this disease. Copyright © 2017 Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.