Recent advances in quantum machine learning (QML) have demonstrated the potential of quantum algorithms to tackle complex classification tasks beyond the capabilities of classical methods. In this study, we propose a novel quantum clustering (QC)-based framework for the classification of DNA sequences. Building upon methods of QC, we extend the paradigm to biological sequence data by encoding nucleotide sequences into a quantum-compatible feature space using one-hot, k-mer, and amplitude encodings. Our approach combines quantum evolution under a potential landscape defined by data density with a hybrid quantum-classical variational classifier to distinguish between DNA sequence classes. We implement the full pipeline on near-term quantum hardware using variational quantum circuits and simulate performance using Qiskit and PennyLane frameworks. Our method demonstrates robust performance in classifying synthetic and biological DNA datasets, achieving competitive accuracy with enhanced clustering resolution in high-dimensional quantum Hilbert spaces. This work represents the application of QC to DNA classification and highlights the promise of quantum-enhanced bioinformatics in the NISQ era.