An investigation of the unsteady magnetohydrodynamic fluid flow with heat and mass transfer of a viscous, incompressible, electrically conducting and Newtonian fluid past a vertical plate embedded in a porous medium taking into account induced magnetic field, first order chemical reaction and thermal radiation effect is carried out. The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient and unconditionally stable finite difference scheme of the Crank-Nicholson type. A computer software is used to iteratively solve the partial differential equations. The numerical solutions for fluid velocity, induced magnetic field, species concentration and fluid temperatures are depicted graphically. The effect of various non-dimensional parameters on the fluid flow profiles are discussed and physical interpretation given. Applications of the study include laminar magneto aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.