The study of the coupling between structural and dynamical heterogeneities in nanostructured systems is essential for the design of hybrid materials with the desired properties. Here, we use atomistic molecular dynamics simulations to closely examine the dynamical heterogeneities in nanostructured single-molecule nanoparticles consisting of mikto-arm star copolymers with poly(ethylene oxide), PEO, and polystyrene, PS, arms. The particles exhibit an internally nanostructured morphology, resembling either "Janus-like" or "patchy-like" morphology when the functionality of the stars varies. The differences in the local environment result in strong intramolecular dynamical heterogeneities. In the proximity of the star core, geometric constraints promote unfavorable PEO:PS contacts that lead to a behavior similar to dynamically asymmetric miscible polymer blends or disordered copolymers. In contrast, further away from the core, the nanosegregation induces segmental dynamics very similar to the one found in the homopolymer star analogues.