We propose a method to reveal axions and axion-like particles based on interferometric measurement of neutron beams. We consider an interferometer in which the neutron beam is split in two sub-beams propagating in regions with differently oriented magnetic fields. The beam paths and the strength of the magnetic fields are set in such a way that all the contributions to the phase difference but the one due to axion-induced interactions are removed. The resulting phase difference is directly related to the presence of axions. Our results show that such a phase is in principle detectable with neutron interferometry, possibly proving the existence of axions and axion-like particles.