The deregulation of the FOXM1 transcription factor is a key molecular alteration in ovarian cancer, contributing to the development and progression of ovarian cancer via activation of the target genes. As such, FOXM1 is a highly attractive therapeutic target in the treatment of ovarian cancer, but there has been no clinically tested FOXM1 inhibitor to date. We investigated in this study the effects of domatinostat, a class I-selective HDAC inhibitor currently in the clinical stage of development as a cancer therapeutic, on the expression of FOXM1 and viability of ovarian cancer cells. Cell viability, as well as protein and mRNA expression of FOXM1 and its transcriptional target survivin, was examined after domatinostat treatment of TOV21G and SKOV3 ovarian cancer cell lines in the absence or presence of cisplatin and paclitaxel. The effect of FOXM1 knockdown on survivin expression and those of genetic and pharmacological inhibition of survivin alone or in combination with the chemotherapeutic agents on cell viability were also examined. Domatinostat reduced the protein and mRNA expression of FOXM1 and survivin and also the viability of ovarian cancer cells alone and in combination with cisplatin or paclitaxel at clinically relevant concentrations. Knockdown experiments showed survivin expression was dependent on FOXM1 in ovarian cancer cells. Survivin inhibition was sufficient to reduce the viability of ovarian cancer cells alone and in combination with the chemotherapeutic agents. Our findings suggest that domatinostat, which effectively targets the FOXM1–survivin axis required for the viability of ovarian cancer cells, is a promising option for the treatment of ovarian cancer.