Recently, the magnetic moment/Mn, M, in MnxSi1−x was measured to be 5.0 Bohr magneton/Mn, at x=0.1%. To understand this observed M, we investigate several MnxSi1−x models of alloys using first-principles density functional methods. The only model giving M=5.0 was a 513-atom cell having the Mn at a substitutional site, and Si at a second-neighbor interstitial site. The observed large moment is a consequence of the weakened d-p hybridization between the Mn and one of its nearest neighbor Si atoms, resulting from the introduction of the second-neighbor interstitial Si. Our result suggests a way to tune the magnetic moments of transition metal doped semiconductors.