Analyzing medical images and videos with computer-aided algorithms provides important benefits in the diagnosis and treatment of diseases. Especially in recent years, the increasing developments in deep learning algorithms have provided continuous improvement in subjects such as speed, performance and hardware need in the processing of medical data. Examination of medical data, which may require advanced expertise, using deep learning algorithms has begun to be widely used as a secondary tool in the decision-making process of physicians. Tracking the movements of the fetus and recognizing its planes in ultrasound (US) videos is an important parameter in evaluating the health of the baby. In this study, a YOLOv5 deep learning network based method is proposed to identify fetal anatomical planes from fetal ultrasound and to detect their movements. First of all, a dataset of videos containing 16-20 weeks of fetal movements is created in the study. In the next step, the fetal head, arm, heart and body are identified and tracking using the deep-SORT algorithm on the labeled data. In the experimental studies conducted on ultrasound videos within the scope of the study, using the YOLOv5 algorithm, head, body, heart and arm are recognized with 95.04%, 94.42%, 88.31% and 83.23% F1-score, respectively. In addition, ultrasonic video movements of the head, heart and body of the fetus are followed and the trajectories and patterns of the movements are extracted. Thus, the detection of fetal movements from the movement patterns transformed into a two-dimensional plane is achieved.