Cells that grow in confined spaces eventually build up mechanical compressive stress. This growth-induced pressure (GIP) decreases cell growth. GIP is important in a multitude of contexts from cancer, to microbial infections, to biofouling, yet our understanding of its origin and molecular consequences remains limited. Here, we combine microfluidic confinement of the yeast Saccharomyces cerevisiae, with rheological measurements using genetically encoded multimeric nanoparticles (GEMs) to reveal that growth-induced pressure is accompanied with an increase in a key cellular physical property: macromolecular crowding. We develop a fully calibrated model that predicts how increased macromolecular crowding hinders protein expression and thus diminishes cell growth. This model is sufficient to explain the coupling of growth rate to pressure without the need for specific molecular sensors or signaling cascades. As molecular crowding is similar across all domains of life, this could be a deeply conserved mechanism of biomechanical feedback that allows environmental sensing originating from the fundamental physical properties of cells.