Abnormal cell growth in the brain characterizes brain tumors, which are primarily diagnosed through histopathological examination. Non-invasive neuroimaging techniques, such as MRI, provide critical diagnostic insights; however, the size and complexity of MRI data pose challenges for effective analysis. While traditional AI methods are effective in medical data analysis, factors such as the expansion of high-resolution medical datasets and noise levels in the data impact the diagnostic process. Recent studies have shown that the application of quantum AI technologies in healthcare not only addresses these issues, but also accelerates complex data analyses, providing a significant advantage, especially in dealing with heterogeneous and unevenly distributed datasets. In this study, a quantum deep neural network (QDNN) model is proposed to distinguish four different classes—glioma, meningioma, pituitary tumors, and cases without tumors—based on data from 7023 individuals obtained from the Kaggle open data portal, aiming for the highest accuracy. During preprocessing, image enhancement techniques were applied using the OpenCV library to optimize data quality. Subsequently, the proposed QDNN model was employed for classification. In the model, amplitude encoding was utilized to map MR image data from classical space to quantum Hilbert space, followed by a multi-layer parameterized quantum circuit (multi-layer PQC). The multi-layer PQC model consists of single-qubit Rx gates, along with a CNOT gate that provides circular entanglement between qubits. As a result, the proposed model achieved final training loss and validation loss values of 0.61 and 0.64, respectively, while the training accuracy and validation accuracy values were 0.76 and 0.77, respectively. When compared to a classical DNN model with a similar number of parameters, the proposed quantum model demonstrates superior performance in terms of both accuracy and total processing time. These results highlight the potential of quantum AI in improving diagnostic accuracy in biomedical imaging.