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Minimally invasive surgery (MIS) is among the preferred procedures for treating a number of ailments as patients benefit from fast recovery and reduced blood loss. The trade-off is that surgeons lose direct visual contact with the surgical site and have limited intra-operative imaging techniques for real-time feedback. Computer vision methods as well as segmentation and tracking of the tissues and tools in the video frames, are increasingly being adopted to MIS to alleviate such limitations. So far, most of the advances in MIS have been focused on laparoscopic applications, with scarce literature on knee arthroscopy. Here for the first time, we propose a new method for the automatic segmentation of multiple tissue structures for knee arthroscopy. The training data of 3868 images were collected from 4 cadaver experiments, 5 knees, and manually contoured by two clinicians into four classes: Femur, Anterior Cruciate Ligament (ACL), Tibia, and Meniscus. Our approach adapts the U-net and the U-net++ architectures for this segmentation task. Using the cross-validation experiment, the mean Dice similarity coefficients for Femur, Tibia, ACL, and Meniscus are 0.78, 0.50, 0.41, 0.43 using the U-net and 0.79, 0.50, 0.51, 0.48 using the U-net++. While the reported segmentation method is of great applicability in terms of contextual awareness for the surgical team, it can also be used for medical robotic applications such as SLAM and depth mapping.