A numerical study on the thermal and mass transfer of magnetohydrodynamic (MHD) flow of a viscous non-Newtonian fluid over a stretching surface has been taken into account. A concentration-dependent viscosity fluid model has been employed to study the non-Newtonian behavior. Cattaneo-Christov heat flux model (CCHFM) has been incorporated to study thermal and mass transport. Hybrid nanofluid has been used to increase the thermal performance. Consequences of thermal radiation, Ohmic heating, and slip boundary conditions have been scrutinized. Governing equations have been transposed into a dimensionless system of ordinary differential equations (ODEs) by employing appropriate similarity transposition. Numerical scheme bvp4c in MATLAB has been incorporated to find the numerical solutions. Consequences of various controlling parameters on fluidic flow, thermal, and concentration profiles have been reported with graphs and tables. Analogy of the presented results with previously published data has been established.