Significance The behavior of cells is strongly affected by the mechanics of their surroundings. In tissues, cells interact with the extracellular matrix, a 3D network of biopolymers with a highly nonlinear elastic response. We introduce a method exploiting this matrix nonlinearity to infer mechanical stresses in 3D. Using this method, we demonstrate that cell contractility induces large stresses, which generate a massive stiffness gradient over an extended region in 3D matrices of collagen, fibrin, and Matrigel. Our work highlights the importance of nonlinear matrix mechanics at the microscopic scale and suggests a concrete mechanism through which cells can control their microenvironment and mechanically communicate with each other.