An exact solution to the problem of MHD transient free convection and mass transfer flow of a viscous, incompressible, and electrically conducting fluid past a suddenly started infinite vertical plate taking into account the thermal diffusion as well as the thermal radiation is presented. Assuming the medium to be nonscattered and the fluid to be nongray, emitting–absorbing, and optically thin radiation limit properties, the equations governing the flow and heat and mass transfer are solved by Laplace transform technique. The expressions for the velocity field, the concentration field, the skin friction at the plate in the direction of the flow, and the coefficient of heat transfer and mass transfer from the plate to the fluid have been obtained, and their numerical values for different values of the physical parameters involved in the problem have been demonstrated in graphs and tables, and these are physically interpreted. It is found that the thermal radiation retards the fluid flow whereas the Soret effect accelerates the flow. The viscous drag on the plate is increased under the Soret and magnetic field effects whereas the thermal radiation reduces the skin friction. Further, the rate of heat transfer at the plate increases under thermal radiation effect. Also, in the presence of radiation, the Soret effect results in a steady increase in the mass flux from the fluid to the plate.