Large neutrino detectors like IceCube monitor for core-collapse supernovae using low-energy (MeV) neutrinos with a detection reach from a supernova neutrino burst to the Magellanic Cloud. However, some models predict the emission of high-energy neutrinos of GeV–TeV from core-collapse supernovae through the interaction of ejecta with circumstellar material with energies of TeV–PeV produced through choked jets. In this paper, we explore the detection horizon of IceCube for core-collapse supernovae using high-energy neutrinos from these models. We examine the potential of two high-energy neutrino data samples from IceCube, one that performs best in the northern sky and one that has better sensitivity in the southern sky. We demonstrate that, by using high-energy neutrinos from core-collapse supernovae, the detection reach can be extended to the megaparsec range, far beyond what is accessible through low-energy neutrinos. Looking ahead to IceCube-Gen2, this reach will be extended considerably.