This work is focused on the examination of the effect of thermal radiation on the heat and mass transfer characteristics of an incompressible electrically conducting fluid squeezed between two parallel plates in the presence of a transverse magnetic field. Using the similarity transformation, the governing system of nonlinear partial differential equations is transformed into similarity equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the Runge–Kutta sixth-order integration scheme. Numerical results are presented through graphs and tables for pertinent parameters to show interesting aspects of the solution.