Mechanical stress can influence cell proliferation in vitro, but whether it makes a significant contribution to growth control in vivo, and how it is modulated and experienced by cells within developing tissues, has remained unclear. Here we report that differential growth reduces cytoskeletal tension along cell junctions within faster-growing cells. We propose a theoretical model to explain the observed reduction of tension within faster-growing clones, supporting it by computer simulations based on a generalized vertex model. This reduced tension modulates a biomechanical Hippo pathway, decreasing recruitment of Ajuba LIM protein and the Hippo pathway kinase Warts, and decreasing the activity of the growth-promoting transcription factor Yorkie. These observations provide a specific mechanism for a mechanical feedback that contributes to evenly distributed growth, and we show that genetically suppressing mechanical feedback alters patterns of cell proliferation in the developing Drosophila wing. By providing experimental support for the induction of mechanical stress by differential growth, and a molecular mechanism linking this stress to the regulation of growth in developing organs, our results confirm and extend the mechanical feedback hypothesis.