  Gamma-ray bursts (GRBs) are rare but powerful explosions displaying highly
relativistic jets. It has been suggested that a significant fraction of the
much more frequent core-collapse supernovae are accompanied by comparably
energetic but mildly relativistic jets, which would indicate an underlying
supernova--GRB connection. We calculate the neutrino spectra from the decays of
pions and kaons produced in jets in supernovae, and show that the kaon
contribution is dominant and provides a sharp break near 20 TeV, which is a
sensitive probe of the conditions inside the jet. For a supernova at 10 Mpc, 30
events above 100 GeV are expected in a 10 s burst in the IceCube detector.
