The histone deacetylase (HDAC) inhibitor vorinostat has received significant attention in recent years as an ‘epigenetic’ drug used to treat solid tumors. However, its mechanisms of action are not entirely understood, particularly with regard to its interaction with the aberrations in 3D nuclear structure that accompany neoplastic progression. We investigated the impact of vorinostat on human esophageal epithelial cell lines derived from normal, metaplastic (pre-cancerous), and malignant tissue. Using a combination of novel optical computed tomography (CT)-based quantitative 3D absorption microscopy and conventional confocal fluorescence microscopy, we show that subjecting malignant cells to vorinostat preferentially alters their 3D nuclear architecture relative to non-cancerous cells. Optical CT (cell CT) imaging of fixed single cells showed that drug-treated cancer cells exhibit significant alterations in nuclear morphometry. Confocal microscopy revealed that vorinostat caused changes in the distribution of H3K9ac-marked euchromatin and H3K9me3-marked constitutive heterochromatin. Additionally, 3D immuno-FISH showed that drug-induced expression of the DNA repair gene MGMT was accompanied by spatial relocation toward the center of the nucleus in the nuclei of metaplastic but not in non-neoplastic cells. Our data suggest that vorinostat’s differential modulation of 3D nuclear architecture in normal and abnormal cells could play a functional role in its anti-cancer action.