This paper investigates the linear stability of the interface between two viscous, incompressible, electrically conducting fluids in the presence of a uniform magnetic field parallel to the interface, focusing on the suppression of the Kelvin–Helmholtz instability. The classical instability arises when two fluid layers of different densities move with different velocities, leading to the amplification of small disturbances at their interface. By incorporating magnetohydrodynamic (MHD) effects into the linearized Navier–Stokes and Maxwell equations, we derive a modified dispersion relation that accounts for both magnetic tension and velocity shear. The results show that a sufficiently strong magnetic field can completely stabilize the interface by counteracting the shear-induced vorticity. The critical magnetic field required for stabilization depends on the density contrast and relative velocity of the two layers. The analysis has implications for astrophysical plasma flows, liquid metal processing, and oceanic or atmospheric shear layers.