Shallow donor far infrared spectroscopy was carried out on n-type CdTe thin layers grown by molecular beam epitaxy on semi-insulating GaAs substrates. Indium doped layers of 0.5 μm thickness were deposited on a nominally undoped CdTe buffer layer with the thickness between 0.5 and 7 μm. We show that (i) the layers investigated are unintentionally doped with a native donor of an unknown origin with the chemical shift different from that of In; (ii) the shape of the spectral lines shows that the CdTe part of a structure is composed of layers characterized by either a small or a large disorder; (iii) the main sources of the disorder are structural defects originating from the CdTe/GaAs interface and propagating into CdTe layers over a distance of about 4 μm.