  Under the fossil field hypothesis of the origin of magnetar magnetic fields,
the magnetar inherits its magnetic field from its progenitor. We show that
during the supernova of such a progenitor, protons may be accelerated to \sim
10^4 GeV as the supernova shock propagates in the magnetic stellar envelope.
Inelastic nuclear collisions of these protons produce a flash of high-energy
neutrinos arriving a few hours after thermal (10 MeV) neutrinos. The neutrino
flash is characterized by energies up to O(100) GeV and durations seconds to
hours, depending on the progenitor: those from smaller Type Ibc progenitors are
typically shorter in duration and reach higher energies compared to those from
larger Type II progenitors. A Galactic Type Ib supernova leaving behind a
magnetar remnant will yield up to \sim 160 neutrino induced muon events in
Super-Kamiokande, and up to \sim 7000 in a km^3 class detector such as IceCube,
providing a means of probing supernova models and the presence of strong
magnetic fields in the stellar envelope.
