Thin ${}^{57}$Fe layers evaporated onto an MgO(100) single-crystal substrate and covered by an evaporated MgO layer were studied by low-temperature conversion electron M\"ossbauer spectroscopy. The temperature dependence of the spectra indicates superparamagnetic behavior below 8 ML nominal thickness of the Fe layer signaling a cluster-type growth mode. The low-temperature hyperfine fields are consistent with a model that defines two types of metallic Fe atoms: bulklike and interfacial ones. Formation of FeO or (Fe,Mg)O at the interface layer is not observed. The sample with a 4-ML Fe layer when grown over a cleaved MgO substrate shows almost perfect perpendicular magnetization, as locally probed at 15 K by the hyperfine magnetic field, while random magnetization orientation and lower blocking temperature is observed in the case of a polished substrate. The perpendicular anisotropy observed at low temperature is attributed to mechanical stresses arising from the epitaxial relation and the different temperature dilatation of the subsequent layers.