The physical properties of the extracellular matrix (ECM) regulate the behavior of several cell types; yet, mechanisms by which cells recognize and respond to changes in these properties are not clear. For example, breast epithelial cells undergo ductal morphogenesis only when cultured in a compliant collagen matrix, but not when the tension of the matrix is increased by loading collagen gels or by increasing collagen density. We report that the actin-binding protein filamin A (FLNa) is necessary for cells to contract collagen gels, and pull on collagen fibrils, which leads to collagen remodeling and morphogenesis in compliant, low-density gels. In stiffer, high-density gels, cells are not able to contract and remodel the matrix, and morphogenesis does not occur. However, increased FLNa-beta1 integrin interactions rescue gel contraction and remodeling in high-density gels, resulting in branching morphogenesis. These results suggest morphogenesis can be "tuned" by the balance between cell-generated contractility and opposing matrix stiffness. Our findings support a role for FLNa-beta1 integrin as a mechanosensitive complex that bidirectionally senses the tension of the matrix and, in turn, regulates cellular contractility and response to this matrix tension.