Electronic properties of tetragonal MoSi2 thin films are studied by the first-principles method. The results show that the MoSi2 film is always metallic, and its density of states and electronic structure are gradually close to their bulk counterpart as the film thickness increases. We further show that the three-atomic-layer film with the lowest energy is magnetic and has a magnetic moment of 0.33 B for its unit cell, and the film becomes non-magnetic when its thickness is more than three atomic layers. Moreover, we investigate the electronic properties of the three-atomic-layer MoSi2 films under unilateral and bilateral hydrogenation and find that the film with unilateral hydrogenation is magnetic and has a magnetic moment of 0.26 B, while the film with bilateral hydrogenation is non-magnetic. The spin polarizations for the films without hydrogenation and unilateral hydrogenation are 30% and 33%, respectively. These results suggest that three-atomic-layer MoSi2 film is metallic or magnetic when it is under suspension or grown on substrate, indicating its potential applications in nanoscale electronic and spintronic devices.