Single-chain nanoparticles (SCNPs) are a new class of macromolecular objects, synthesized through purely intramolecular cross-linking of single polymer chains. We use a multiscale hydrodynamics simulation approach to study, for the first time, SCNPs under shear flow. We investigate the case of irreversible SCNPs (permanent cross-links) in dilute solution. SCNPs emerge as a novel class of macromolecular objects with response to shear distinct from other systems such as linear chains, star polymers, rings, or dendrimers. This is evidenced by the observed set of scaling exponents for the shear rate dependence of the SCNP static and dynamic properties. Surprisingly, these exponents are, at most, marginally dependent on the specific topology of the SCNP (globular or sparse), suggesting that they are inherently related to the network-like character of the molecular architecture and not to its specific connectivity. At high Weissenberg numbers the dynamics of the sparse SCNPs is dominated by tumbling motion. Coexistence of tumbling and tank treading is observed for the most globular SCNPs.