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Due to significant advances in nanomedicine, magnetic nanoparticles (MNs) have emerged as a promising carrier in targeted magnetic drug delivery (TMDD) systems. Therefore, this paper presents a computational model for optimized magnetic navigation of MNs coated with the anticancer drugs inside the blood vessels. A mixture of blood and MNs is represented as a one-phase solution in the majority of TMDD models. The preceding two-phase models are usually one-way coupled, i.e., the blood flow has a significant influence on the MNs flow. However, the inverse effect of the MNs on the blood flow is not taken into account. To overcome these limitations, the MNs in a blood vessel are simulated by a two-phase (solid–liquid) flow governed by two-way coupled momentum and temperature equations for the blood flow and the MNs. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical method on a finite-difference grid. The model, validated by the experimental results, has been applied to analyze the formation of vortices relative to the magnetic force and the drag force and the zones of TMDD, where the velocity of the blood flow is low and the velocity of the MNs is high toward the magnet. The model has been verified against the existing models and the experimental data. The numerical results show that the magnetohydrodynamics slows down the blood flow and smooths vortices created by Ferrohydrodynamics. The size of the drug-loaded MNs on the velocity and the temperature of the blood has been evaluated.