This study investigates the steady two-dimensional natural-convection flow and heat and mass transfer of a Cu–Al2O3/water thixotropic hybrid nanofluid over a vertically stretching sheet. The boundary-layer model incorporates magnetic effects, thermal radiation, heat generation, viscous dissipation, Joule heating, melting, chemical reaction, species diffusion, and motile microorganisms. By applying suitable similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and solved numerically using MATLAB bvp4c. The results show that the magnetic field suppresses the velocity profile, whereas melting enhances it. Temperature increases with the heat source parameter but decreases with radiation and melting, while nanoparticle concentration declines with higher Schmidt number and chemical reaction. In addition, microorganism concentration decreases with the bioconvection Lewis number and increases with the Peclet number and microorganism concentration difference parameter.