Using the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we determine for the first time the average neutron rms radius of ^{133}Cs and ^{127}I. We obtain the practically model-independent value R_{n}=5.5_{-1.1}^{+0.9} fm using the symmetrized Fermi and Helm form factors. We also point out that the COHERENT data show a 2.3σ evidence of the nuclear structure suppression of the full coherence.