Nearly perpendicular magnetic hyperfine fields have been observed for the first time in the Ag "spacers" of Fe/Ag multilayers using low temperature nuclear orientation of (110)Ag(m) at 6 mK. At the same time, vibrating sample magnetometry measurements at temperatures down to 4 K have shown the magnetic anisotropy of the Fe to be in plane. The direction of the Ag hyperfine field is thus noncollinear (nearly orthogonal) to the Fe anisotropy. These results are compared with full potential linearized augmented plane wave calculations using the wien97 code.