Fifteen ATLAS-MPX devices are installed in the ATLAS detector and cavern by the ATLAS-MPX collaboration. This network of sensors provides a real-time measurement of the composition of the radiation field inside the ATLAS detector and its cavern. This article reports calibration measurements of the thermal and fast neutron detection efficiency of the ATLASMPX devices. In order to detect neutrons, the 300 μm thick silicon sensor of each device was covered with mask of 6LiF and polyethylene (PE) converters. Efficiency measurements were performed with calibrated natural thermal neutron source; calibrated 252Cf and 241AmBe sources. Fast neutrons with monochromatic energy of 14 MeV were delivered by a Van de Graaff (VDG) accelerator beam. The devices showed a mean efficiency of 1.02x10-2 for thermal neutrons (6LiF-Si region), 3.17x10-4 for 252Cf, 7.51x10-4 for 241AmBe and 1.81x10-3 for 14 MeV neutrons (PE-Si region) while all background signal generated by X-rays, Gamma-rays and electrons was fully suppressed by appropriate discrimination level. These data allow the estimation of the neutron fluxes in ATLAS and provide initial data for precise simulation of the detector environment at the ATLAS-MPX devices locations.