Despite great progress in engineering functional tissues for organ repair, including the heart, an invasive surgical approach is still required for their implantation. Here, we designed an elastic and microfabricated scaffold using a biodegradable polymer (poly(octamethylene maleate (anhydride) citrate)) for functional tissue delivery via injection. The scaffold’s shape memory was due to the microfabricated lattice design. Scaffolds and cardiac patches (1 cm × 1 cm) were delivered through an orifice as small as 1 mm, recovering their initial shape following injection without affecting cardiomyocyte viability and function. In a subcutaneous syngeneic rat model, injection of cardiac patches was equivalent to open surgery when comparing vascularization, macrophage recruitment and cell survival. The patches significantly improved cardiac function following myocardial infarction in a rat, compared with the untreated controls. Successful minimally invasive delivery of human cell-derived patches to the epicardium, aorta and liver in a large-animal (porcine) model was achieved.