Two-dimensional (2D) high-aspect-ratio sheet-like materials are a broad class of synthetic ultra-thin sheet-like solids whose rapid pace of development motivates systematic study of their biological effects and safe design. A challenge for this effort is the large number of new materials and their chemical diversity. Recent work suggests that many 2D materials will be thermodynamically unstable and thus non-persistent in biological environments. Such information could inform and accelerate safety assessment, but experimental data to confirm the thermodynamic predictions are lacking. Here we propose a framework for early hazard screening of nanosheet materials based on biodissolution studies in reactive media, specially chosen for each material to match chemically feasible degradation pathways. Simple dissolution and in vitro tests allow grouping of nanosheet materials into four classes: A, potentially biopersistent; B, slowly degradable (>24-48 hours); C, biosoluble with potentially hazardous degradation products; and D, biosoluble with low-hazard degradation products. The proposed framework is demonstrated through an experimental case study on MoO3 nanoribbons, which have a dual 2D/1D morphology and have been reported to be stable in aqueous stock solutions. The nanoribbons are shown to undergo rapid dissolution in biological simulant fluids and in cell culture, where they elicit no adverse responses up to 100 μg ml−1 dose. These results place MoO3 nanoribbons in Class D, and assigns them a low priority for further nanotoxicology testing. We anticipate use of this framework could accelerate the risk assessment for the large set of new powdered 2D nanosheet materials, and promote their safe design and commercialization.