We report the results of a search for inelastic scattering of weakly interacting massive particles (WIMPs) off I127 nuclei using NaI(Tl) crystals with a data exposure of 97.7 kg·years from the COSINE-100 experiment. The signature of inelastic WIMP-I127 scattering is a nuclear recoil accompanied by a 57.6 keV γ-ray from the prompt deexcitation, producing a more energetic signal compared to the typical WIMP nuclear recoil signal. We found no evidence for this inelastic scattering signature and set a 90% confidence level upper limit on the WIMP-proton spin-dependent, inelastic scattering cross section of 1.2×10-37 cm2 at the WIMP mass 500 GeV/c2.