The Drosophila egg chamber is an organ composed of a somatic epithelium that covers a germline cyst. After egg-chamber formation, the germline cells grow rapidly without dividing while the surface of the epithelium expands by cell proliferation [1, 2]. The mechanisms that coordinate growth and morphogenesis of the two tissues are not known. Here we identify a role for the actomyosin cytoskeleton in this process. We show that myosin activity is restricted to the epithelium's apical surface, which is facing the growing cyst. We demonstrate that the epithelium collapses in the absence of myosin activity and show that the force that deforms the epithelium originates from the growing cyst. Thus, myosin activity maintains epithelial shape by balancing the force emanating from cyst growth. Further, our data indicate that cyst growth induces cell division in the epithelium. In addition, we show how apical restriction of myosin activity is controlled. Myosin is activated at the apical cortex by localized Rho kinase and inhibited at the basolateral cortex by PP1beta9C. In addition, our data indicate that active myosin is apically anchored by the Baz/Par-6/aPKC complex.