57Fe-Mössbauer studies of superconducting Rb_0.8Fe _1.6Se_2.0 with T_C = 32.4 K were performed on single-crystalline and polycrystalline samples in the temperature range 4.2-295 K. They reveal the presence of 88% magnetic and 12% nonmagnetic Fe2⁺ species with the same polarization dependence of their hyperfine spectra. The magnetic species are attributed to the 16i sites of the √5×√ 5×1 superstructure and the nonmagnetic Fe species to a nanosized phase observed in recent structural studies of superconducting K_xFe _2-ySe₂ systems rather than to the vacant 4d sites in the √5×√5×1 superstructure. The 57Fe spectrum of a single-crystalline sample in an external field of 50 kOe applied parallel to the crystallographic c axis confirms the antiferromagnetic order between the fourfold ferromagnetic Fe(16i) supermoments and the absence of a magnetic moment at the Fe sites in the minority phase. A discussion of all spectral information and comparison with superconducting FeSe provides convincing evidence that the nanoscale phase separation is monitored by Mössbauer spectroscopy in Rb_0.8Fe_1.6Se_2.0.