The n̄-Fe absorption cross section sigma(nbarFe) has been measured at LEAR (the Low Energy Antiproton Ring at CERN) using tagged n̄'s produced in the p̄p → n̄n charge-exchange reaction. With incident p̄ momenta of 875 and 545 MeV/c sigma(nbarFe) has been measured in the momentum interval between 125 and 780 MeV/c, in a region where only a few measurements presently exist. The overall statistical and systematic errors range from 20 to 5%; the normalisation error is less than 3%. The measured cross sections are well reproduced by a parametrisation a+b/p, with a = 0.680 ± 0.051 barn and b = 0.228 ± 0.024 barn·GeV/c.