In this study, we examined the influence of an induced magnetic field on the steady magneto hydrodynamic (MHD) flow of an electrically conducting fluid over a vertical porous plate within a porous medium. It is assumed that the magnetic Reynolds number of the MHD flow is sufficiently large, necessitating the consideration of the induced magnetic field. The governing equations of motion, along with their boundary conditions, are rendered dimensionless through similarity transformations. The resulting transformed equations are solved numerically using the fourth-order Runge-Kutta method in conjunction with the shooting technique. The effects of relevant parameters on the velocity, temperature, and induced magnetic field profiles are analyzed graphically, and the physical implications are discussed in detail.