High-energy neutrinos generated in collimated jets inside the progenitors of gamma-ray bursts (GRBs) have been related to the events detected by IceCube. These neutrinos, produced by hadronic interactions of Fermi-accelerated protons with thermal photons and hadrons in internal shocks, are the only signature when the jet has not broken out or failed. Taking into account that the photon field is thermalized at keV energies and the standard assumption that the magnetic field maintains a steady value throughout the shock region (with a width of 1010–1011 cm in the observed frame), we study the effect of thermal and magnetized plasma generated in internal shocks on the neutrino oscillations. We calculate the neutrino effective potential generated by this plasma, the effects of the envelope of the star, and the vacuum on the path to Earth. By considering these three effects, the two (solar, atmospheric and accelerator parameters) and three neutrino mixing, we show that although GeV–TeV neutrinos can oscillate resonantly from one flavour to another, a non-significant deviation of the standard flavour ratio (1: 1: 1) could be expected on Earth.