The viscometry of minute amounts of liquid has been in high demand as a novel tool for medical diagnosis and biological assays. Various microrheological techniques have shown the capability to handle small volumes. However, as the liquid volume decreases down to nanoliter scale, increasingly dominant surface effects complicate the measurement and analysis, which remain a challenge in microrheology. Here, we demonstrate an atomic force microscope-based platform that determines the viscosity of single sessile drops of 1 nanoliter Newtonian fluids. We circumvent interfacial effects by measuring the negative-valued shear elasticity, originating from the retarded fluidic response inside the drop. Our measurement is independent of the liquid-boundary effects, and thus is valid without a priori knowledge of surface tension or contact angle, and consistently holds at a 1 milliliter-scale volume. Importantly, while previous methods typically need a much larger ‘unrecoverable’ volume above 1 microliter, our simple platform uses only ∼1 nanoliter. Our results offer a quantitative and unambiguous methodology for viscosity measurements of extremely minute volumes of Newtonian liquids on the nanoliter scale.