The present investigation deals with magnetic drug targeting in a microvessel of radius 5 μm using two-phase fluid model. The microvessel is divided into the endothelial glycocalyx layer wherein the blood obeys Newtonian character and a core region wherein the blood obeys the non-Newtonian Casson fluid character. The carrier particles, bound with nanoparticles and drug molecules, are injected into the vascular system upstream from the malignant tissue and are captured at the tumor site using a local applied magnetic field near the tumor position. Brinkman model is used to characterize the permeable nature of the inner wall of the microvessel. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size and shape of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel, are considered in the present problem. The system of coupled equations is solved to obtain the trajectories of the carrier particle in the noninvasive case.