High harmonic generation in crystalline solids has been examined so far on the basis of one-body energy-band structures arising from electron itineracy in a periodic potential. Here, we show the emergence of high harmonic generation signals which are attributed to the dynamics of many-body states in a low-dimensional correlated electron system. An interacting fermion model and its effective pseudospin model on a one-dimensional dimer-type lattice are analyzed. Observed high harmonic generation signals in a spontaneously symmetry-broken state, where charge densities are polarized inside of dimer units, show threshold behavior with respect to light amplitude and are interpreted in terms of tunneling and recombination of kink-antikink excitations in an electric field.