We report the first time-resolved high-harmonic spectroscopy (TR-HHS) study of a chemical bond rearrangement. We investigate the transient change of the high-harmonic signal from 1,3-cyclohexadiene (CHD), which undergoes ring-opening and isomerizes to 1,3,5-hexatriene (HT) upon photoexcitation. We associated the harmonic yield variation with the changes in the molecule's electronic state and vibrational frequencies, which are caused by isomerization. This showed us that the electronic excited state of CHD created through two-photon absorption of 3.1 eV photons relaxes almost completely within 100 fs to the electronic ground state of CHD with vibrational excitation. Subsequently, the molecule isomerizes to HT (i.e., ring-opening occurs, around 400 fs after the excitation). The present results demonstrate that TR-HHS, which can track both electronic and nuclear dynamics, is a powerful tool for studying ultrafast photochemical reactions.