Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Context. Long gamma-ray bursts (GRBs) are associated with the gravitational collapse of very massive stars. The central engine of a GRB can collimate relativistic jets that propagate inside the stellar envelope. The shock waves produced when the jet disrupts the stellar surface are capable of accelerating particles up to very high energies. Aims. If the jet has hadronic content, neutrinos will be produced via charged pion decays. The main goal of this work is to estimate the neutrino emission produced in the region close to the surface of the star, taking pion and muon cooling into account, along with subtle effects arising from neutrino production in a highly magnetized medium. Methods. We estimate the maximum energies of the different kinds of particles and solve the coupled transport equations for each species. Once the particle distributions are known, we calculate the intensity of neutrinos. We study the different effects on the neutrinos that can change the relative weight of different flavors. In particular, we consider the effects of neutrino oscillations, and of neutrino spin precession caused by strong magnetic fields. Results. The expected neutrino signals from the shocks in the uncorking regions of Population III events is very weak, but the neutrino signal produced by Wolf-Rayet GRBs with z < 0.5 is not far from the level of the atmospheric background. Conclusions. The IceCube experiment does not have the sensitivity to detect neutrinos from the implosion of the earliest stars, but a number of high-energy neutrinos may be detected from nearby long GRBs. The cumulative signal should be detectable over several years (similar to 10 yr) of integration with the full 86-string configuration.558ANPCyT [BID 1728/OC -AR PICT-2012-00878]CONICET [PIP 0078/2010]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)[AYA 2010-21782-C03-01]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)ANPCyT [BID 1728/OC -AR PICT-2012-00878]CONICET [PIP 0078/2010]FAPESP [2012/16389-1][AYA 2010-21782-C03-01]