We report the results of a search for the inelastic scattering of weakly interacting massive particles (WIMPs) in the XENON1T dark matter experiment. Scattering off 129Xe is the most sensitive probe of inelastic WIMP interactions, with a signature of a 39.6 keV deexcitation photon detected simultaneously with the nuclear recoil. Using an exposure of 0.83 tonne-years, we find no evidence of inelastic WIMP scattering with a significance of more than 2σ. A profile-likelihood ratio analysis is used to set upper limits on the cross section of WIMP-nucleus interactions. We exclude new parameter space for WIMPs heavier than 100 GeV/c2, with the strongest upper limit of 3.3×10−39 cm2 for 130 GeV/c2 WIMPs at 90% confidence level.