The non-stationary Karpman–Washimi ponderomotive force and self-generated magnetic field in an unmagnetized system are investigated in the context of nonextensive distribution based on the kinetic theory. The ponderomotive force, magnetization, and radiation power are obtained as functions of the nonextensive parameter q, wave frequency, and wave number. It is shown that the presence of high-velocity electrons leads to an increase in temporal and spatial variation parts of ponderomotive force, magnetization, and radiation power. Furthermore, the results indicate that the self-generated magnetic field driven by the Karpman–Washimi ponderomotive force primarily manifests as small-scale and low-frequency magnetic field.