The rise of autonomous vehicles (AVs) has led to an increased reliance on vehicle-to-vehicle (V2V) communication networks to ensure real-time information sharing, situational awareness, and cooperative decision-making. However, the integration of quantum computing into cybersecurity threatens the cryptographic foundations upon which current V2V communication protocols rely. As quantum computers grow closer to practical implementation, traditional public-key encryption schemes—such as RSA and ECC—are rendered vulnerable to attacks from quantum algorithms like Shor’s and Grover’s. This review explores the necessity of adopting quantum-resistant cryptographic protocols to secure V2V communication frameworks. The study critically examines post-quantum cryptographic algorithms, including lattice-based, hash-based, code-based, multivariate polynomial, and isogeny-based schemes, with a focus on their applicability to latency-sensitive and resource-constrained vehicular environments. Furthermore, the paper evaluates the performance, scalability, and implementation challenges of integrating these cryptographic primitives into real-time autonomous systems. Case studies of pilot implementations and emerging research are reviewed to highlight the practicality of these protocols in vehicular edge computing and 5G-enabled automotive networks. The paper concludes by proposing a forward-looking roadmap for standardization and integration of quantum-resilient cryptography in intelligent transportation systems (ITS), ensuring long-term data integrity, authentication, and privacy across V2V infrastructures.