We study third-harmonic generation (THG) in an excitonic insulator (EI) described in a two-band correlated electron model. Employing the perturbative expansion with respect to the external electric field, we derive the THG susceptibility taking into account the collective dynamics of the excitonic order parameter. In the inversion-symmetric EI, the collective order parameter motion is activated at second order of the external field and its effects arise in THG. We find three peaks in the THG susceptibility at energies $hbar Omega = Delta_g/3$, $Delta_g/2$, and $Delta_g$, where $Delta_g$ is the bandgap. While the THG response at $Delta_g/3$ is caused by three-photon excitation of the independent particle across the bandgap, the latter two peaks involve the effects of the collective motion activated at second order. The resulting resonant peaks are prominent in particular in the BCS regime but they become less significant in the BEC regime. We demonstrate that the resonant peaks originated by the collective excitations are observable in the temperature profile of the THG intensity. Our study suggests that the THG measurement should be promising for detecting the excitonic collective nature of materials.
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