Networks of natural protein nanofibrils, such as cytoskeletal filaments, control the shape and the division of cells, yet mimicking this functionality in a synthetic setting has proved challenging. Here, we demonstrate that artificial networks of protein nanofibrils can induce controlled deformation and division of all-aqueous emulsion droplets with budding-like morphologies. We show that this process is driven by the difference in the immersional wetting energy of the nanofibril network, and that both the size and the number of the daughter droplets formed during division can be controlled by modulating the fibril concentration and the chemical properties of the fibril network. Our results demonstrate a route for achieving biomimetic division with synthetic self-assembling fibrils and offer an engineered approach to regulate the morphology of protein gels.