We use PFG NMR to measure hindered self-diffusion of spherical, monodisperse diffusional nanoprobes in a polysaccharide network. These nanoprobes have different diameters in the 1–10 nm range, but identical inert (PEG) surfaces. We use Johnson’s model of particle self-diffusion in fibrous networks to estimate the polymer strand thickness and to obtain a measure for the network mesh size. Johnson’s model takes into account the obstruction effect, and the degree of obstruction is independent from the arrangement of the polymer strands at low polymer concentrations. Probe particles with different sizes provide consistent predictions of strand thickness in this concentration regime. This allows us to infer a structural length scale close to the average mesh size of the polymer network.