Blockchain-based Vehicular Ad-hoc Network (VANET) is widely considered as secure communication architecture for a connected transportation system. With the advent of quantum computing, there are concerns regarding the vulnerability of this architecture against cyber-attacks. In this study, a potential threat is investigated in a blockchain-based VANET, and a corresponding quantum cyber-attack is developed. Specifically, a quantum impersonation attack using Quantum-Shor algorithm is developed to break the Rivest-Shamir-Adleman (RSA) encrypted digital signatures of VANET and thus create a threat for the trust-based blockchain scheme of VANET. A blockchain-based VANET, vehicle-to-everything (V2X) communication, and vehicular mobility are simulated using OMNET++, the extended INET library, and vehicles-in-network simulation (VEINS) along with simulation of urban mobility (SUMO), respectively. A small key RSA based message encryption is implemented using IBM Qiskit, which is an open-source quantum software development kit. The findings reveal that the quantum cyber-attack, example, impersonation attack is able to successfully break the trust chain of a blockchain-based VANET. This highlights the need for a quantum secured blockchain.