  Growing evidence from multi-wavelength observations of extragalactic
supernovae (SNe) has established the presence of dense circumstellar material
in Type II SNe. Interaction between the SN ejecta and the circumstellar
material should lead to diffusive shock acceleration of cosmic rays and
associated high-energy emission. Observation of high-energy neutrinos along
with the MeV neutrinos from SNe will provide unprecedented opportunities to
understand unanswered questions in cosmic-ray and neutrino physics. We show
that current and future neutrino detectors can identify high-energy neutrinos
from an extragalactic SN in the neighborhood of the Milky Way. We present the
prospects for detecting high-energy neutrino minibursts from SNe in known local
galaxies, and demonstrate how the network of multiple high-energy neutrino
detectors will extend the horizon for the identification of high-energy SN
neutrinos. We also discuss high-energy neutrino emission from SN 2023ixf.
