The author presents the influence of Arrhenius activation energy and binary chemical reaction on an unsteady magnetohydrodynamics Williamson nanofluid with motile gyrotactic micro‐organisms. The governing equations are converted to coupled ordinary differential equations with similarity transformations and the fifth‐order Runge‐Kutta Fehlberg method and the shooting algorithm is applied to solve these equations using the appropriate boundary conditions. A detailed investigation considering the effects of different physical parameters on the profiles like velocity, temperature, concentration, and density of motile gyrotactic micro‐organisms was done and plotted graphically. It is found that the thermal boundary layer enhances for the chemical reaction rate and the solutal boundary layer increases for activation energy. Furthermore, the nondimensional Williamson parameter reduces for the velocity profile. The author studied the wall temperature gradient of different fluids and found that temperature gradient decreased for the present study. Comparisons of the present result with published work were done to verify the present code. © 2020 Wiley Periodicals, Inc.