We report 65 T magnetoabsorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor . The strongly field-dependent and distinct energy shifts of the , , and excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the exciton states agree remarkably well with detailed numerical simulations using the nonhydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields, the nearly linear diamagnetic shifts of the weakly bound and excitons provide a direct experimental measure of the exciton’s reduced mass .