J/psi production in d + Au and p + p collisions at square root of S(NN) = 200 GeV has been measured by the PHENIX experiment at rapidities -2.2 < y < +2.4. The cross sections and nuclear dependence of J/psi production versus rapidity, transverse momentum, and centrality are obtained and compared to lower energy p + A results and to theoretical models. The observed nuclear dependence in d + Au collisions is found to be modest, suggesting that the absorption in the final state is weak and the shadowing of the gluon distributions is small and consistent with Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-based parametrizations that fit deep-inelastic scattering and Drell-Yan data at lower energies.