We report on theoretical calculations of the optical conductivity of Ba(Fe_1−xCo_x)₂As₂, as obtained from density functional theory within the full-potential linear augmented plane-wave method. A thorough comparison with experiment shows that we are able to reproduce most of the observed experimental features, in particular, a magnetic peak located at about 0.2 eV, which we ascribe to antiferromagnetic ordered magnetic stripes. We also predict a large in-plane anisotropy of this feature, which agrees very well with measurements on detwinned crystals. The effect of Co doping, as well as the dependence of plasma frequency on the magnetic order, is also investigated.