Nuclear shadowing is observed in the per-nucleon cross sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001<xBj<0.56 and 0.1<Q2<80 GeV2. The data are consistent with no significant ν or Q2 dependence at fixed xBj. As xBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.