The wavelength of the 57Fe Mössbauer radiation is measured with a relative uncertainty of 0.19 ppm by using almost exact Bragg backscattering from a reference silicon crystal. Its value is determined as lambda(M) = 0.860 254 74(16)x10(-10) m. The corresponding Mössbauer photon energy is E(M) = 14 412.497(3) eV. The wavelength of the 57Fe Mössbauer radiation is easily reproducible with an accuracy of at least 10(-11)lambda(M) and could be used as a length standard of atomic dimensions.