This work examines the continuous magnetohydrodynamic boundary layer flow of a nanofluid across a stretching surface, considering the influences of Brownian motion, thermophoresis, and chemical reactions in the context of suction/injection. A similarity transformation is utilized to convert the controlling partial differential equations into a system of coupled nonlinear ordinary differential equations. The equations are numerically solved employing a fourth-order Runge-Kutta method alongside the shooting methodology. Particular emphasis is placed on examining the impact of the Brownian motion parameter (Nb) on the nanoparticle concentration profile. The findings indicate that augmenting Nb improves the diffusive transport of nanoparticles, thus thickening the concentration boundary layer. The method's accuracy and convergence are confirmed, and the resulting profiles are graphically analyzed for different values of Nb. These findings elucidate the dynamics of nanofluid transport under nonlinear rheological and electromagnetic influences..