Addressing the origin of the observed diffuse astrophysical neutrino flux is one of the main challenges in the context of the neutrino astronomy nowadays. Among several astrophysical sources, Gamma-Ray Bursts (GRBs) are considered interesting candidates to be explored. Indeed, being the most powerful explosions observable in the Universe, they are potentially able to achieve the energetics required to reproduce the neutrino flux. Thus, they are expected to provide at least some contribution to the astrophysical diffuse neutrino flux. Within the framework of the fireball model, mesons can be produced during photo-hadronic interactions occurring in the internal shocks between shells emitted by the central engine; from their decays, high-energy gamma rays and neutrinos are expected to be generated. Within this scenario, the results of a stacked search for astrophysical muon neutrinos performed in space and time coincidence with 784 GRBs in the period 2007-2017 using ANTARES data are presented. The neutrino flux expectation from each GRB detectable by ANTARES was calculated in the framework of the classical internal shock model. Given the absence of coincident neutrinos, the contribution of the detected GRB population to the neutrino diffuse flux is constrained to be less than 10% around 100 TeV. In addition, the systematic uncertainties on the diffuse flux are computed by propagating to the stacked limit the uncertainties on the model parameters for each individual burst.