Handwritten digit recognition in regional scripts, such as Devanagari, is crucial for multilingual document digitization, educational tools, and the preservation of cultural heritage. The script's complex structure and limited annotated datasets pose significant challenges to conventional models. This paper introduces the first hybrid quantum-classical architecture for Devanagari handwritten digit recognition, combining a convolutional neural network (CNN) for spatial feature extraction with a 10-qubit variational quantum circuit (VQC) for quantum-enhanced classification. Trained and evaluated on the Devanagari Handwritten Character Dataset (DHCD), the proposed model achieves a state-of-the-art test accuracy for quantum implementation of 99.80% and a test loss of 0.2893, with an average per-class F1-score of 0.9980. Compared to equivalent classical CNNs, our model demonstrates superior accuracy with significantly fewer parameters and enhanced robustness. By leveraging quantum principles such as superposition and entanglement, this work establishes a novel benchmark for regional script recognition, highlighting the promise of quantum machine learning (QML) in real-world, low-resource language settings.