Modern vehicles can be considered sophisticated computer systems in motion, where new technologies enhance on-board comfort and safety but also increase internal complexity, particularly regarding communication networks. The Controller Area Network (CAN), the most widespread in-vehicle communication protocol, must face important security challenges, such as the lack of confidentiality and authentication mechanisms. This lack makes vehicles vulnerable to several cyber-threats. In this work, we analyze the security weaknesses of CAN. Again, we contribute to improving CAN by defining a novel security model to face quantum threats. In particular, by applying the CRYSTALS-Kyber primitive for secure session key sharing and encrypting communications with symmetric primitives, our model ensures the confidentiality of CAN communication and protection against quantum threats. Experimental results demonstrate that the proposed solution can be applied to conventional in-vehicle networks without significantly affecting the efficiency or reliability of vehicles.