New optical sensors with a segmented photosensitive area are being developed for the next generation of neutrino telescopes at the South Pole. In addition to increasing sensitivity to high-energy astrophysical neutrinos, we show that this will also lead to a significant improvement in sensitivity to MeV neutrinos, such as those produced in core-collapse supernovae (CCSN). These low-energy neutrinos can provide a detailed picture of the events after stellar core collapse, testing our understanding of these violent explosions. We present studies on the event-based detection of MeV neutrinos with a segmented sensor and, for the first time, the potential of a corresponding detector in the deep ice at the South Pole for the detection of extra-galactic CCSN. We find that exploiting temporal coincidences between signals in different photocathode segments, a $$27\ \mathrm {M}_{\odot }$$ $27M_{\odot }$ progenitor mass CCSN can be detected up to a distance of 341 kpc with a false detection rate of $${0.01}\,\hbox {year}^{-1}$$ $0.01{\text{year}}^{-1}$ with a detector consisting of 10,000 sensors. Increasing the number of sensors to 20,000 and reducing the optical background by a factor of 70 expands the range such that a CCSN detection rate of 0.1 per year is achieved, while keeping the false detection rate at $${0.01}\,{\hbox {year}^{-1}}$$ $0.01{\text{year}}^{-1}$ .