We report on the first electron nuclear double-resonance investigation of an interstitial deep-level defect in silicon. For interstitial iron the superhyperfine interactions with six shells of neighbor nuclei comprising 42 silicon atoms could be resolved and determined. The localization of the two paramagnetic $3d$ electrons ($3{d}^{8}$) at the ${\mathrm{Fe}}_{i}^{0}$ atom could be estimated to be between 80% and 95%. The superhyperfine data are discussed with a simple model for the defect wave function. It is shown that exchange polarization plays a major role in determining the superhyperfine interactions.