We present a first-principles investigation of the structural, electronic, and magnetic properties of the pristine and Fe-doped α-MnO₂ using density-functional theory with extended Hubbard functionals. The onsite U and intersite V Hubbard parameters are determined from first principles and self-consistently using density-functional perturbation theory in the basis of Löwdin-orthogonalized atomic orbitals. Among the ferromagnetic and four types of antiferromagnetic (AFM) orderings for the pristine α-MnO₂ we find the C2-AFM spin configuration to be the most energetically favorable, in agreement with the experimentally observed AFM state. The computed lattice parameters, magnetic moments, and band gaps are overall in good agreement with the experimental ones when both the onsite and intersite Hubbard corrections are included. For the Fe-doped α-MnO₂ two types of doping are considered: Fe insertion in the 2 × 2 tunnels and partial substitution of Fe for Mn. The calculated formation energies show that Fe insertion is energetically favorable, in agreement with experiments. We find that both types of doping preserve the C2 AFM spin configuration of the host lattice. The oxidation state of Fe is found to be 2+ and 4+ in the case of the interstitial and substitutional doping, respectively, while the oxidation state of Mn is 4+ in both cases. This work opens a door for accurate studies of other Mn oxides and complex transition-metal compounds when the localization of 3d electrons occurs in the presence of strong covalent interactions with ligands.