Medical image classification has been a fundamental task in computer-aided diagnosis. In this work, we propose a hybrid quantum-classical deep learning framework that integrates a parameterized quantum layer into the ResNet-18 architecture for medical image classification. Our experiments are conducted on the OrganMNIST-Axial, OrganMNIST-Coronal, and OrganMNIST-Sagittal datasets from the MedMNIST v2 collection, each consisting of $28 \times 28$ grayscale images representing different organ sections. The quantum layer is implemented as a 6-qubit variational quantum circuit (VQC) that partially replaces the classical fully connected module, enabling the network to exploit quantum feature mapping and entanglement for enhanced nonlinear representation learning. This architectural modification reduces the number of classical trainable parameters by approximately 44% compared with the original ResNet-18 while preserving its representational capacity. We evaluate the proposed QResNet18 against classical baselines to investigate its potential advantages in terms of accuracy, robustness, and parameter efficiency. Experimental results demonstrate that the hybrid quantum-classical model achieves competitive or superior performance while maintaining a significantly reduced parameter count, highlighting the feasibility and promise of quantumenhanced medical image classification.