Of concern in the paper is a study on blood flow through a porous segment of an artery subject to the action of an external magnetic field. Effects of viscosity variation and variable hematocrit as well as velocity-slip at the arterial wall have been duly taken care of in the study. A model has been developed to perform the study by using the principles of magnetohydrodynamics (MHD). The model has been analysed theoretically by employing suitable mathematical methods. Analytical expressions have been derived for the velocity, minute expenditure of blood (volumetric flow rate), wall shear stress and pressure gradient. The said physical variables are computed by using a specific set of values of the various parameters involved in the analysis. This serves as an illustration of the validity of the mathematical model developed in the paper. The computational results are presented graphically. The study also provides important insight into the effects of slip velocity on blood velocity, wall shear stress and pressure gradient. The study further shows that the flow of blood in a porous artery is significantly influenced by the action of an external magnetic field.