The ovary is a vital component of the female reproductive system, housing numerous spherical structures known as follicles. These follicles play a crucial role in diagnosing various female health conditions such as infertility, Polycystic Ovarian Syndrome (PCOS), and Ovarian Cancer. Presently, the evaluation of follicle size, shape, and count relies on the manual examination of ultrasound images of the ovaries, a process prone to errors, labour-intensiveness, and time consumption. To enhance this monitoring process performed by radiologists and doctors, researchers have proposed several segmentation methods over the past few decades. Nevertheless, there is still room for improvement in the segmentation process, specifically in accurately isolating the Region of Interest (ROI) in terms of shape, position, and count. Moreover, as accuracy rates are improved, it becomes critical to minimize the occurrence of false identifications. Addressing these challenges necessitates the extraction of a comprehensive set of features from the target region while maintaining a sharp focus on the ROI. In this context, this research introduces an automated approach that leverages deep learning techniques for the segmentation of ovarian follicles. The foundation of this method is a U-Net model, strengthened by the incorporation of attention mechanisms and residual connections to amplify its performance. To validate the effectiveness of this approach, experiments were conducted using the USOVA 3D dataset. The experimental results validate the superiority of the proposed method, referred to as the Attention Residual U-Net (ARU Net), compared to conventional U-Net models, Attention U-Net models, and state-of-the-art models. Notably, the Attention Residual U-Net achieved an impressive accuracy rate of 97.65% using a rigorous 5-fold cross-validation. Additionally, the model exhibited outstanding performance with Recall, Precision, and Dice Coefficient scores of 89.45%, 92.13%, and 69.26%, respectively.