As herbarium specimens are increasingly becoming digitised and accessible in online repositories, advanced computer vision techniques are being used to extract information from them. The presence of certain plant organs on herbarium sheets is useful information in various scientific contexts and automatic recognition of these organs will help mobilise such information. In our study, we use deep learning to detect plant organs on digitised herbarium specimens with Faster R-CNN. For our experiment, we manually annotated hundreds of herbarium scans with thousands of bounding boxes for six types of plant organs and used them for training and evaluating the plant organ detection model. The model worked particularly well on leaves and stems, while flowers were also present in large numbers in the sheets, but were not equally well recognised.