Abstract: In the past decade, a new class of bright transient radio sources with millisecond duration has been discovered. The origin of these so-called fast radio bursts (FRBs) is still a mystery, despite the growing observational efforts made by various multiwavelength and multimessenger facilities. To date, many models have been proposed to explain FRBs, but neither the progenitors nor the radiative and the particle acceleration processes at work have been clearly identified. In this paper, we assess whether hadronic processes may occur in the vicinity of the FRB source. If they do, FRBs may contribute to the high-energy cosmic-ray and neutrino fluxes. A search for these hadronic signatures was carried out using the ANTARES neutrino telescope. The analysis consists in looking for high-energy neutrinos, in the TeV-PeV regime, that are spatially and temporally coincident with the detected FRBs. Most of the FRBs discovered in the period 2013-2017 were in the field of view of the ANTARES detector, which is sensitive mostly to events originating from the Southern hemisphere. From this period, 12 FRBs were selected and no coincident neutrino candidate was observed. Upper limits on the per-burst neutrino fluence were derived using a power-law spectrum, dN/DE nu proportional to E-nu(-gamma), for the incoming neutrino flux, assuming spectral indexes gamma = 1.0, 2.0, 2.5. Finally, the neutrino energy was constrained by computing the total energy radiated in neutrinos, assuming different distances for the FRBs. Constraints on the neutrino fluence and on the energy released were derived from the associated null results.