Anterior cruciate ligament (ACL) tear is a sports-related trauma that can have a significant impact on the performance and long-term health of athletes. Timely and accurate identification of such injuries is essential to facilitate effective treatment and recovery. In this research, a new approach for the diagnosis of tears in the anterior cruciate ligament (ACL) is presented through the use of a Convolutional Neural Network (CNN), which is optimized using the Modified Golden Search Algorithm (MGSA). The proposed method is capable of extracting significant features from Magnetic Resonance Imaging (MRI) images of the knee using an optimized CNN architecture. The hybrid golden search algorithm showed a superior accuracy of 99.6% compared to other methods. These findings demonstrate the efficacy of this strategy in optimizing the CNN structure for the provided objective. The findings of the study show that CNN optimized using MGSA model can serve as an effective mechanism for detecting ACL tears in knee MRI images. This has the potential to improve the accuracy and efficiency of ACL injury diagnosis and encourage timely action and excellent rehabilitation results.