We report constraints on light dark matter (DM) models using ionization signals in the XENON1T experiment. We mitigate backgrounds with strong event selections, rather than requiring a scintillation signal, leaving an effective exposure of (22±3) tonne day. Above ∼0.4 keV_{ee}, we observe <1 event/(tonne day keV_{ee}), which is more than 1000 times lower than in similar searches with other detectors. Despite observing a higher rate at lower energies, no DM or CEvNS detection may be claimed because we cannot model all of our backgrounds. We thus exclude new regions in the parameter spaces for DM-nucleus scattering for DM masses m_{χ} within 3-6 GeV/c^{2}, DM-electron scattering for m_{χ}>30 MeV/c^{2}, and absorption of dark photons and axionlike particles for m_{χ} within 0.186-1 keV/c^{2}.