The nuclear quadrupole moment (NQM) of the Ipi = 3/2(-) excited nuclear state of 57Fe at 14.41 keV, important in Mössbauer spectroscopy, is determined from the large-scale nuclear shell-model calculations for 54Fe, 57Fe, and also from the electronic ab initio and density functional theory calculations including solid state and electron correlation effects for the molecules Fe(CO)(5) and Fe(C5H5)(2). Both independent methods yield very similar results. The recommended value is 0.15(2) e b. The NQM of the isomeric 10+ in 54Fe has also been calculated. The new NQM values for 54Fe and 57Fe are consistent with the perturbed angular distribution data.