We have observed for the first time the nuclear magnetic resonance (NMR) of 57Fe in iron powder with an average size of the metal core of particles on the order of 10 mm. The signal relaxation times have been determined, which differ significantly from the corresponding values in the bulk material. Dependences of the spin echo signal amplitude on the magnetic field have been measured. It is suggested that features of the observed NMR signal can be explained assuming a monodomain structure of iron nanoparticles. Using Mössbauer spectroscopy as a supplementary technique, the ratio of oxide and metal phase fractions in the powder has been estimated. It is shown that the NMR and Mössbauer spectroscopy data are consistent with the results of electron-microscopic observations and confirm nanostructural character of the substance studied.