Alzheimer’s Disease (AD) is a well-recognized brain ailment that can be identified by examining brain tissues specifically segmenting the hippocampus from brain MRI. This type of dementia is one among the most common dementia, that people experience, which emphasizes the urgent need for new techniques to identify the illness at an early stage. Early diagnosis of brain illnesses and disorders is made possible by precisely delineating the hippocampus. We propose a Hippocampus Segmentation-Enhanced U-Net (HCS-EUNET) model to separate the hippocampal regions in brain MRI with a Stochastic Optimization Method that combines the momentum of Nesterov’s which can enhance Stochastic Gradient Descent’s (SGD) speed of convergence and provide precise segmentation. This includes the segmentation capabilities of complex structures from medical images such as MRIs, which also have the advantage of capturing local and comprehensive information. This work aims to increase the precision of the segmentation, robustness, and generalization capacity and minimize the loss. Accuracy, Loss, Dice, and IoU have been employed to compare the prediction performance of the proposed method that outperforms the existing method. AD is detected with the dissimilarity of the left and right hippocampus in MR brain images. The proposed method has a significant opportunity for physicians or radiologists to use as a computer-aided tool to detect AD and assist them in an accurate and early diagnosis using MR brain images.