We present measurements of νμ charged-current cross section ratios on carbon, iron, and lead relative to a scintillator (CH) using the fine-grained MINERvA detector exposed to the NuMI neutrino beam at Fermilab. The measurements utilize events of energies 2<Eν<20GeV, with Eν©=8GeV, which have a reconstructed μ- scattering angle less than 17° to extract ratios of inclusive total cross sections as a function of neutrino energy Eν and flux-integrated differential cross sections with respect to the Bjorken scaling variable x. These results provide the first high-statistics direct measurements of nuclear effects in neutrino scattering using different targets in the same neutrino beam. Measured cross section ratios exhibit a relative depletion at low x and enhancement at large x. Both become more pronounced as the nucleon number of the target nucleus increases. The data are not reproduced by GENIE, a conventional neutrino-nucleus scattering simulation, or by the alternative models for the nuclear dependence of inelastic scattering that are considered. © 2014 American Physical Society.