We propose far-infrared photodetectors with the graphene nanoribbon (GNR) array as the photosensitive element and the black phosphorus (bP) base layer (BL). The operation of these GNR infrared photodetectors (GNR-IPs) is associated with the interband photogeneration of the electron–hole pairs in the GNR array followed by the tunneling injection of either electrons or holes into a wide gap bP BL. The GNR-IP operating principle is akin to that of the unitraveling-carrier photodiodes based on the standard semiconductors. Due to a narrow energy gap in the GNRs, the proposed GNR-IPs can operate in the far-, mid-, and near-infrared spectral ranges. The cut-off photon energy, which is specified by the GNR energy gap (i.e., is dictated by the GNR width), can be in the far-infrared range, being smaller that the energy gap of the bP BL of Δ_G  ≃  300  meV. Using the developed device models of the GNR-IPs and the GNR-IP terahertz photomixers, we evaluate their characteristics and predict their potential performance. The speed of the GNR-IP response is determined by rather short times: the photocarrier try-to-escape time and the photocarrier transit time across the BL. Therefore, the GNR-IPs could operate as terahertz photomixers. The excitation of the plasma oscillations in the GNR array might result in a strong resonant photomixing.