Social Anxiety Disorder (SAD) significantly impacts individuals' daily lives and relationships. The conventional methods for SAD detection involve physical consultations and self-reported questionnaires, but they have limitations such as time consumption and bias. This paper introduces video analysis as a promising method for early SAD detection. Specifically, we present a new approach for detecting SAD in individuals from various bodily features extracted from the video data. We conducted a study to collect video data of 92 participants performing impromptu speech in a controlled environment. Using the video data, we studied the behavioral change in participants' head, body, eye gaze, and action units. By applying a range of machine learning and deep learning algorithms, we achieved an accuracy rate of up to 74\% in classifying participants as SAD or non-SAD. Video-based SAD detection offers a non-intrusive and scalable approach that can be deployed in real-time, potentially enhancing early detection and intervention capabilities.