Type IIn supernovae (SNe), a rare subclass of core collapse SNe, explode in dense circumstellar media that have been modified by the SNe progenitors at their last evolutionary stages. The interaction of the freely expanding SN ejecta with the circumstellar medium gives rise to a shock wave propagating in the dense SN environment, which may accelerate protons to multi-PeV energies. Inelastic proton-proton collisions between the shock-accelerated protons and those of the circumstellar medium lead to multimessenger signatures. Here, we evaluate the possible neutrino signal of Type IIn SNe and compare with IceCube observations. We employ a Monte Carlo method for the calculation of the diffuse neutrino emission from the SN IIn class to account for the spread in their properties. The cumulative neutrino emission is found to be ∼10 per cent of the observed IceCube neutrino flux above 60 TeV. Type IIn SNe would be the dominant component of the diffuse astrophysical flux, only if 4 per cent of all core collapse SNe were of this type and 20-30 per cent of the shock energy was channeled to accelerated protons. Lower values of the acceleration efficiency are accessible by the observation of a single Type IIn SN as a neutrino point source with IceCube using up-going muon neutrinos. Such an identification is possible in the first year following the SN shock breakout for sources within 20 Mpc.