The natural extracellular matrix (ECM) within tissues is physically contracted and remodeled by cells, allowing the collective shaping of functional tissue architectures. Synthetic materials that facilitate self-assembly similar to natural ECM are needed for cell culture, tissue engineering, and in vitro models of development and disease. To address this need, we develop fibrous hydrogel assemblies that are stabilized with photocrosslinking and display fiber density–dependent strain-responsive properties (strain stiffening and alignment). Encapsulated mesenchymal stromal cells locally contract low fiber density assemblies, resulting in macroscopic volumetric changes with increased cell densities and moduli. Because of properties such as shear-thinning and self-healing, assemblies can be processed into microtissues with aligned ECM deposition or through extrusion bioprinting and photopatterning to fabricate constructs with programmed shape changes due to cell contraction. These materials provide a synthetic approach to mimic features of natural ECM, which can now be processed for applications in biofabrication and tissue engineering.