The equilibrium sites and electronic structure of interstitial hydrogen or muonium in Si clusters are calculated using the approximate ab initio method of partial retention of diatomic differential overlap and ab initio Hartree-Fock with minimum, expanded and polarized basis sets. The clusters range in size from Si2H6 to Si44H42. The interstitial sites considered include the tetrahedral, hexagonal, antibonding and bond-centered sites, as well as more exotic locations such as the C, the M, and the umbrella sites (which is similar to an antibonding site, but in a distorted environment). Lattice relaxations and distortions are included up to second-nearest neighbors. Basis-set effects are discussed. The most stable site is the relaxed bond-centered site, which is the location of anomalous muonium. The associated energy level is deep in the gap. In contrast to diamond, bond-centered hydrogen in Si vibrates primarily along the bond. The tetrahedral interstitial site is the only other minimum of the energy. It is not deep enough to localize a proton which probably diffuses along 111 directions. The energy level associated with interstitial H at the tetrahedral site is below the top of the valence band.