The modern research aims to explore the influence of free stream flow on the motion of MHD Non-Newtonian nanofluid through a permeable extending surface in a three-dimensional domain. The primary goal of this research is to examine the significance of distinct fluid parameters, including Casson fluid parameter β, free stream velocity parameter λ, Brownian motion parameter Nb, magnetic parameter M, Prandtl number Pr, thermophoresis parameter Nt, Lewis number Le on distribution of velocity, concentration of nanoparticle and temperature. When similarity variables are incorporated into the set of governing partial differential equations, the equations are modified into a set of ordinary differential equations. Runge–Kutta fourth order is employed with the help of shooting approach in order to achieve the computational approach of the model that has been reduced. Numerical values of physical characteristics, like that the Nusselt number, the Sherwood number, and skin friction, have been assessed contrary to numerous parameters and disclosed in tables for the subject of engineering. Results for distribution of temperature, velocity and concentration of nanoparticles are explored in detail, including their rate of convergence. The principal results of the research revealed that the influence of both Casson fluid and magnetic parameter on the distribution of velocity exhibits a pattern of decline. Additionally, the effects of Brownian motion parameter on temperature demonstrate a rising pattern, while its impact on concentration distribution shows a diminishing trend. The use of permeable materials has shown that the heat transport process along an expanding surface prevents thermal loss and promotes the cooling process, which is a significant outcome of the study. The findings of this research have numerous applications in biomedical engineering and are useful for the analysis of fluids that are not Newtonian under various conditions. The recent study in the three-dimensional extending region is important for the development of novel industrial processes involving nanoparticles and the idea of magnetohydrodynamics flow of non-Newtonian fluids in existence of free stream flow.