We compute the nuclear corrections to the proton-deuteron Drell-Yan cross section for inclusive dilepton production, which, when combined with the proton-proton cross section, is used to determine the flavor asymmetry in the proton sea, dbar - ubar. In addition to nuclear smearing corrections that are known to be important at large values of the nucleon's parton momentum fraction x_N, we also consider dynamical off-shell nucleon corrections associated with the modifications of the bound nucleon structure inside the deuteron, which we find to be significant at intermediate and large x_N values. We also provide estimates of the nuclear corrections at kinematics corresponding to existing and planned Drell-Yan experiments at Fermilab and J-PARC which aim to determine the dbar/ubar ratio for x