Suction/injection is a mechanical effect and used to control the energy losses in the boundary layer region by reducing the drag on the surface. In this study, unsteady MHD flow of Brinkman-type fluid with suction/injection, heat absorption, and chemical reaction is investigated and an analytical solution is established. The corresponding results for temperature, concentration, and velocity fields are obtained with the help of the Laplace transformation method analytically. The physical effects of thermal and mass Grashoff number, Prandtl number, Schmidt number, heat absorption parameter, first-order chemical reaction parameter, suction/injection, Brinkman parameter, and magnetic parameter have been discussed graphically. Finally, it is observed that in the presence of suction effect, fluid’s velocity decreases gradually by increasing the value of suction parameter while show an increasing trend for the increasing value of the injection parameter.