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.