The flux of very high-energy neutrinos produced in our Galaxy by the interaction of accelerated cosmic rays with the interstellar medium is not yet determined. The characterization of this flux will shed light on Galactic accelerator features, gas distribution morphology and Galactic cosmic ray transport. The central Galactic plane can be the site of an enhanced neutrino production, thus leading to anisotropies in the extraterrestrial neutrino signal as measured by the IceCube Collaboration. The ANTARES neutrino telescope, located in the Mediterranean Sea, offers a favorable view of this part of the sky, thereby allowing for a contribution to the determination of this flux. The expected diffuse Galactic neutrino emission can be obtained, linking a model of generation and propagation of cosmic rays with the morphology of the gas distribution in the Milky Way. In this paper, the so-called “gamma model” introduced recently to explain the high-energy gamma-ray diffuse Galactic emission is assumed as reference. The neutrino flux predicted by the “gamma model” depends on the assumed primary cosmic ray spectrum cutoff. Considering a radially dependent diffusion coefficient, this proposed scenario is able to account for the local cosmic ray measurements, as well as for the Galactic gamma-ray observations. Nine years of ANTARES data are used in this work to search for a possible Galactic contribution according to this scenario. All flavor neutrino interactions are considered. No excess of events is observed, and an upper limit is set on the neutrino flux of 1.1 (1.2) times the prediction of the “gamma model,” assuming the primary cosmic ray spectrum cutoff at 5 (50) PeV. This limit excludes the diffuse Galactic neutrino emission as the major cause of the “spectral anomaly” between the two hemispheres measured by IceCube.