Ovarian cancer (OC) develops asymptomatically and escapes diagnosis until advanced stages, the feature contributing to a higher mortality rate. New prospects of OC diagnosis and treatment have been opened in studies of the gene regulation mechanisms that involve long noncoding RNAs (lncRNAs) and identification of the lncRNA genes that are inhibited via methylation of the promoter region. A set of 122 samples of primary OC tumors was examined by methylation specific real-time PCR to assess the methylation level of the lncRNA genes PLUT, SNHG1, SNHG6, SNHG12, and TINCR. A significant increase in their methylation levels was observed in OC (p < 0.001 by the nonparametric Mann-Whitney test). The methylation levels of SNHG6, SNHG12, and TINCR were found to correlate significantly (p < 0.05) with the stage of the tumor process, the histological grade, and metastasis. Downregulation of SNHG6, SNHG12, and TINCR was detected by real-time RT-qPCR, and a significant correlation between methylation and expression was demonstrated for SNHG6 and TINCR (r_s < -0.5, p < 0.001). The respective lncRNA genes were assumed to provide potential epigenetic markers of OC.