Pneumonia poses a significant global health challenge, demanding accurate and timely diagnosis. While deep learning, particularly Convolutional Neural Networks (CNNs), has shown promise in medical image analysis for pneumonia detection, CNNs often suffer from high computational costs, limitations in feature representation, and challenges in generalizing from smaller datasets. To address these limitations, we explore the application of Quanvolutional Neural Networks (QNNs), leveraging quantum computing for enhanced feature extraction. This paper introduces a novel hybrid quantum-classical model for pneumonia detection using the PneumoniaMNIST dataset. Our approach utilizes a quanvolutional layer with a parameterized quantum circuit (PQC) to process 2x2 image patches, employing rotational Y-gates for data encoding and entangling layers to generate non-classical feature representations. These quantum-extracted features are then fed into a classical neural network for classification. Experimental results demonstrate that the proposed QNN achieves a higher validation accuracy of 83.33 percent compared to a comparable classical CNN which achieves 73.33 percent. This enhanced convergence and sample efficiency highlight the potential of QNNs for medical image analysis, particularly in scenarios with limited labeled data. This research lays the foundation for integrating quantum computing into deep-learning-driven medical diagnostic systems, offering a computationally efficient alternative to traditional approaches.