The problem of steady boundary layer flow for Newtonian fluid with variable viscosity and thermal conductivity over stretching wedge in the presence of magnetic field and heat generation (absorption) is studied. The system of governing partial differential equations with the boundary conditions is reduced to a system of ordinary differential equations with appropriate boundary conditions using Lie group. The reduced ordinary differential equations along with the boundary conditions are solved numerically using the fourth order Runge-Kutta method algorithm with the shooting technique. The effects of various parameters on the velocity, the temperature and the concentration profiles are discussed. Finally, the numerical values of the physical quantities, such as local skin-friction coefficient, the local Nusselt number and the local Sherwood number are illustrated graphically.