Multiple viable theoretical models predict heavy dark matter particles with a mass close to the Planck mass, a range relatively unexplored by current experimental measurements. We use 219.4 days of data collected with the XENON1T experiment to conduct a blind search for signals from multiply interacting massive particles (MIMPs). Their unique track signature allows a targeted analysis with only 0.05 expected background events from muons. Following unblinding, we observe no signal candidate events. This Letter places strong constraints on spin-independent interactions of dark matter particles with a mass between 1×1012 and 2×1017 GeV/c2. In addition, we present the first exclusion limits on spin-dependent MIMP-neutron and MIMP-proton cross sections for dark matter particles with masses close to the Planck scale.