First-principles methods are employed to investigate the effect of strain on the carrier effective masses in (111) Si nanowires (SiNWs). It is found that the electron effective masses of SiNWs depend strongly on the applied axial strain. Within a certain range of strain, the electron effective masses are significantly enhanced. Most remarkably, the electron effective masses are anomalous and become infinity at a critical point of strain. This effect is associated with how strain changes the band structure with a single minimum to that with double minima or vice versa. The hole effective masses, on the other hand, decrease with the increase of the tensile strain, as a result of the strain-induced band energy shift in the vicinity of the valence band maximum. It is also shown that the band gaps of SiNWs with diameters ⩾1.16nm increase with the increase of the tensile strain. The tunability of the effective masses and band gaps with strain would be useful in tailoring the transport properties of SiNWs.