In heavy-ion collisions, $J/\psi$ and Drell-Yan production are expected to be affected by nuclear modifications to the free nucleon structure functions. If these modifications, known as shadowing, are proportional to the local nuclear density, the per nucleon cross sections will depend on centrality. Differences in quark and gluon shadowing will lead to a new source of impact parameter dependence of the $J/\psi$ to Drell-Yan production ratio. We calculate this ratio in the CERN NA50 acceptance with several shadowing parameterizations to explore its centrality dependence.