Fractal topologies, which are statistically self-similar over multiple length scales, are pervasive in nature. The recurrence of patterns in fractal-shaped branched objects, such as trees, lungs and sponges, results in a high surface area to volume ratio, which provides key functional advantages including molecular trapping and exchange. Mimicking these topologies in designed protein-based assemblies could provide access to functional biomaterials. Here we describe a computational design approach for the reversible self-assembly of proteins into tunable supramolecular fractal-like topologies in response to phosphorylation. Guided by atomic-resolution models, we develop fusions of Src homology 2 (SH2) domain or a phosphorylatable SH2-binding peptide, respectively, to two symmetric, homo-oligomeric proteins. Mixing the two designed components resulted in a variety of dendritic, hyperbranched and sponge-like topologies that are phosphorylation-dependent and self-similar over three decades (~10 nm-10 μm) of length scale, in agreement with models from multiscale computational simulations. Designed assemblies perform efficient phosphorylation-dependent capture and release of cargo proteins.