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Intra-operative automatic semantic segmentation of knee joint structures can assist surgeons during knee arthroscopy in terms of situational awareness. However, due to poor imaging conditions (e.g., low texture, overexposure, etc.), automatic semantic segmentation is a challenging scenario, which justifies the scarce literature on this topic. In this paper, we propose a novel self-supervised monocular depth estimation to regularise the training of the semantic segmentation in knee arthroscopy. To further regularise the depth estimation, we propose the use of clean training images captured by the stereo arthroscope of routine objects (presenting none of the poor imaging conditions and with rich texture information) to pre-train the model. We fine-tune such model to produce both the semantic segmentation and self-supervised monocular depth using stereo arthroscopic images taken from inside the knee. Using a data set containing 3868 arthroscopic images captured during cadaveric knee arthroscopy with semantic segmentation annotations, 2000 stereo image pairs of cadaveric knee arthroscopy, and 2150 stereo image pairs of routine objects, we show that our semantic segmentation regularised by self-supervised depth estimation produces a more accurate segmentation than a state-of-the-art semantic segmentation approach modeled exclusively with semantic segmentation annotation.