Organic materials for near-infrared (NIR) photodetection are in the focus for developing organic optical-sensing devices. The choice of materials for bulk-type organic photodetectors is limited due to effects like high nonradiative recombination rates for low-gap materials. Here, an organic Schottky barrier photodetector with an integrated plasmonic nanohole electrode is proposed, enabling structure-dependent, sub-bandgap photodetection in the NIR. Photons are detected via internal photoemission (IPE) process over a metal/organic semiconductor Schottky barrier. The efficiency of IPE is improved by exciting localized surface plasmon resonances, which are further enhanced by coupling to an out-of-plane Fabry-Perot cavity within the metal/organic/metal device configuration. The device allows large on/off ratio (>1000) and the selective control of individual pixels by modulating the Schottky barrier height. The concept opens up new design and application possibilities for organic NIR photodetectors.