Clinical diagnosis has become very significant in today’s health system. The most serious disease and the leading cause of mortality globally is brain cancer which is a key research topic in the field of medical imaging. The examination and prognosis of brain tumors can be improved by an early and precise diagnosis based on magnetic resonance imaging. For computer-aided diagnosis methods to assist radiologists in the proper detection of brain tumors, medical imagery must be detected, segmented, and classified. Manual brain tumor detection is a monotonous and error-prone procedure for radiologists; hence, it is very important to implement an automated method. As a result, the precise brain tumor detection and classification method is presented. The proposed method has five steps. In the first step, a linear contrast stretching is used to determine the edges in the source image. In the second step, a custom 17-layered deep neural network architecture is developed for the segmentation of brain tumors. In the third step, a modified MobileNetV2 architecture is used for feature extraction and is trained using transfer learning. In the fourth step, an entropy-based controlled method was used along with a multiclass support vector machine (M-SVM) for the best features selection. In the final step, M-SVM is used for brain tumor classification, which identifies the meningioma, glioma and pituitary images. The proposed method was demonstrated on BraTS 2018 and Figshare datasets. Experimental study shows that the proposed brain tumor detection and classification method outperforms other methods both visually and quantitatively, obtaining an accuracy of 97.47% and 98.92%, respectively. Finally, we adopt the eXplainable Artificial Intelligence (XAI) method to explain the result. Our proposed approach for brain tumor detection and classification has outperformed prior methods. These findings demonstrate that the proposed approach obtained higher performance in terms of both visually and enhanced quantitative evaluation with improved accuracy.