Credit card fraud detection is crucial for financial security which entails identifying unauthorized transactions that can result in significant financial losses. Detection is inherently challenging due to the rarity and indistinguishability of fraudulent transactions from genuine ones, which makes it an anomaly detection problem. Traditional detection systems struggle with the highly imbalanced nature of transaction datasets, where genuine transactions vastly outnumber fraudulent cases. In response to these challenges, we propose a novel detection model utilizing Quantum AutoEncoders-based Fraud Detection (QAE-FD). Our approach leverages quantum computing principles to enhance anomaly detection capabilities by encoding transaction data into compressed quantum states and optimizing the model against a loss function that evaluates the fidelity in flagging fraudulent transactions. The efficacy of the QAE-FD model is tested on a real-world credit card transaction dataset, achieving a G-mean of 0.946 and an AUC of 0.947 which demonstrates superior performance compared to existing models. Our results indicate that QAE-FD has not only higher accuracy in fraud detection but also better computational efficiency. The integration of quantum autoencoders is a promising advancement in the field of anomaly detection for credit card fraud, addressing the limitations of imbalanced datasets and offering a scalable solution for real-time detection systems.