The emergence of quantum computing presents significant challenges for intelligent transportation systems (ITS), which rely on traditional public-key cryptography, demanding both strong security and low-latency operation. This highlights an urgent requirement for post-quantum cryptographic (PQC) algorithms to guarantee long-term protection. However, a direct integration of PQC into ITS may introduce latency and inefficiency, as static implementations cannot adapt to dynamic traffic conditions and may apply excessive security in low-risk contexts, resulting in unnecessary computational overhead, particularly within resource-constrained edge computing environments. To mitigate these issues, the PDRL-PQCS (Predictive Deep Reinforcement Learning for Post-Quantum Cryptography Selection) framework is proposed. This approach employs a Transformer-based module to generate multi-step predictions of traffic flow and computational load, thereby providing proactive contextual awareness. These predictions subsequently inform a deep reinforcement learning (DRL) agent, which dynamically selects optimal parameter configurations for the CRYSTALS-Kyber PQC algorithm in real time, enabling adaptive security-performance balancing across the heterogeneous nodes of an ITS edge computing network. Through this two-stage approach, PDRL-PQCS adapts PQC parameters within defined security bounds to optimally balance security assurance with operational efficiency. An extensive experimental evaluation assesses the framework under three representative traffic scenarios with diverse resource availability and congestion levels. Results indicate that PDRL-PQCS achieves 10%–20% higher overall performance compared to baseline methods across various challenging conditions.