This research focuses on energy convention and mass transpiration in magnetohydrodynamic hybrid nanofluid (Al2O3–Cu) flows driven by a moving surface, which build numerous applications such as inducing hypothermia in cancer tumors, reducing bleeding in severe injuries, and performing magnetic resonance imaging are only a few medical applications applying magnetohydrodynamics A similarity transformation describes the representational construction of the steady two‐dimensional nonlinear partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Above equations subject to corresponding boundary conditions are analytically solved. Specifically, the energy equation with radiation effect is solved analytically using incomplete Gamma function. Moreover, the graphs included physical representations of the measurement can be found in this paper. In summary, our findings demonstrate that mass‐transfer induced slip has a non‐negligible impact on flows driven by a moving sheet. Mass transfer induced slip may even be able to dominate the flow driven effect of the moving sheet by changing the flow directions to flow against the sheet motion and also thermal radiation parameter increases as thermal boundary layer increases.