In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions at the boundary. A non-linear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). For convergent solutions, the obtained ODE system is solved by the use of the BVP4C routine integrated MATLAB package. In addition, the impacts of different influential parameters on motile micro-organisms, temperature, velocity, and concentration profiles are deliberated. The velocity field is observed to be reduced when the slip parameter increases. As the main results, it is demonstrated that the distribution of motile microorganisms against the curvature parameter decreases significantly. Similarly, it is found that the nanofluid parameters (i.e., Brownian motion and thermophoresis parameters) and the Peclet number reduce the motile micro-organisms’ number. On the other hand, it is evidenced that the motile micro-organisms’ distribution can be improved with an increase in bio-convective Schmidt number.