Analytical studies for the problem of flow and heat transfer of an electrically conducting non-Newtonian power-law fluid with low electrical conductivity on a continuously moving infinite porous plate in the presence of viscous dissipation and a uniform transverse magnetic field have been presented. It is found that steady solutions for dimensionless velocity exist only for a fluid in which its power-law index n satisfies 0.5 < n < 1 with suction at the plate. The problem is also solved numerically by using the shooting method. The results show a good agreement between the analytical and the numerical results. The influences of the magnetic parameter, suction parameter, the power-law index, and the Prandtl number on the velocity and temperature profiles are studied. Also the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed and displayed in tables.