The unsteady two-dimensional magnetohydrodynamic heat and mass transfer free convection flow of an incompressible, viscous, electrically conducting polar fluid via a porous medium past a semi-infinite vertical porous moving plate in the presence of a transverse magnetic field with thermal diffusion and heat generation is considered. The plate moves with a constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the polar fluid with a suction velocity varying with time. The mathematical expressions for velocity, angular velocity, temperature and concentration have been obtained, and the solutions are in terms of exponential functions. Representative results for velocity profiles, temperature profiles and skin friction are obtained both in graphical and tabular form for several values of pertinent parameters which are of physical and engineering interest. The method of solution can be applied for small perturbation approximation. The fluids taken in the study are air (Prandtl number Pr=0.71) and water (Prandtl number Pr=7.0). The numerical results of velocity distribution of polar fluids are compared with the corresponding flow problems for a Newtonian fluid. In the absence of magnetic field, the skin friction decreases in air and increases in water. It is also observed that the effect of increasing values of Prandtl number results in a decreasing skin friction which shows that the skin friction is more in air as compared to that in water.