Cellular unjamming is the collective fluidization of cell motion and has been linked to many biological processes, including development, wound repair, and tumor growth. In tumor growth, the uncontrolled proliferation of cancer cells in a confined space generates mechanical compressive stress. However, because multiple cellular and molecular mechanisms may be operating simultaneously, the role of compressive stress in unjamming transitions during cancer progression remains unknown. Here we investigate which mechanism dominates in a dense, mechanically stressed monolayer. We find that long-term mechanical compression triggers cell arrest in benign epithelial cells and enhances cancer cell migration in transitions correlated with cell shape, leading us to examine the contributions of cell-cell adhesion and substrate traction in shape-dependent unjamming transitions. We show that cadherin-mediated cell-cell adhesion regulates differential cellular responses to compressive stress and predominantly controls unjamming transitions in dense monolayers. Importantly, compressive stress does not induce the epithelial—mesenchymal transition in unjammed cells. Using traction force microscopy, traction forces are attenuated in compressed cells in the bulk of the monolayer regardless of cell type and motility. Intercellular adhesion thus is the dominant regulator of compression-induced unjamming transitions and may impact collective cell motion in tumor development and breast cancer progression.