Hydrogels are attractive materials for tissue engineering, but efforts to date have shown limited ability to produce the microstructural features necessary to promote cellular self-organization into hierarchical three-dimensional (3D) organ models. Here we develop a hydrogel ink containing prefabricated gelatin fibres to print 3D organ-level scaffolds that recapitulate the intra- and intercellular organization of the heart. The addition of prefabricated gelatin fibres to hydrogels enables the tailoring of the ink rheology, allowing for a controlled sol-gel transition to achieve precise printing of free-standing 3D structures without additional supporting materials. Shear-induced alignment of fibres during ink extrusion provides microscale geometric cues that promote the self-organization of cultured human cardiomyocytes into anisotropic muscular tissues in vitro. The resulting 3D-printed ventricle in vitro model exhibited biomimetic anisotropic electrophysiological and contractile properties.