In a series of experiments the hyperfine fields of Ag at the interface with Fe were measured in Fe/Ag multilayers using the low temperature nuclear orientation technique. The thickness of the Fe layers was chosen so that the in-plane shape anisotropy would dominate over the perpendicular surface anisotropy. However, for multilayers with a well ordered multilayer structure as measured by x-ray diffraction, the Ag magnetic hyperfine fields were found to be nearly perpendicular to the layer plane. The out-of-plane magnetic structure of the induced Ag magnetic moments has been also supported by vibrating sample magnetometry measurements on the same samples. In addition, the magnitude of the induced Ag hyperfine fields are significantly reduced by roughness. Calculations using WIEN97 confirm that the Ag hyperfine fields are strongly affected by the number of nearest Fe neighbors and their distance.