Advances in engineered hydrogels reveal how cells sense and respond to 3D biophysical cues. However, most studies rely on interfacing a population of cells in a tissue‐scale bulk hydrogel, an approach that overlooks the heterogeneity of local matrix deposition around individual cells. A droplet microfluidic technique to deposit a defined amount of 3D hydrogel matrices around single cells independently of material composition, elasticity, and stress relaxation times is developed. Mesenchymal stem cells (MSCs) undergo isotropic volume expansion more rapidly in thinner gels that present an Arg‐Gly‐Asp integrin ligand. Mathematical modeling and experiments show that MSCs experience higher membrane tension as they expand in thinner gels. Furthermore, thinner gels facilitate osteogenic differentiation of MSCs. By modulating ion channels, it is shown that isotropic volume expansion of single cells predicts intracellular tension and stem cell fate. The results suggest the utility of precise microscale gel deposition to control single cell functions.