Malignancy is associated with changes in cell mechanics that contribute to extensive cell deformation required for metastatic dissemination. We hypothesized that the cell-intrinsic physical factors that maintain epithelial cell mechanics could function as tumor suppressors. Here we show, using optical tweezers, genetic interference, mechanical perturbations, and in vivo studies, that epithelial cells maintain higher plasma membrane (PM) tension than their metastatic counterparts and that high PM tension potently inhibits cancer cell migration and invasion by counteracting membrane curvature sensing/generating BAR family proteins. This tensional homeostasis is achieved by membrane-to-cortex attachment (MCA) regulated by ERM proteins, whose disruption spontaneously transforms epithelial cells into a mesenchymal migratory phenotype powered by BAR proteins. Consistently, the forced expression of epithelial–mesenchymal transition (EMT)-inducing transcription factors results in decreased PM tension. In metastatic cells, increasing PM tension by manipulating MCA is sufficient to suppress both mesenchymal and amoeboid 3D migration, tumor invasion, and metastasis by compromising membrane-mediated mechanosignaling by BAR proteins, thereby uncovering a previously undescribed mechanical tumor suppressor mechanism.