Edge intelligence is a technology that integrates edge computing and artificial intelligence to achieve real-time and localized model generation. Thus, users can receive more precise and personalized services in vehicular ad hoc networks (VANETs) using edge intelligence. However, privacy and security challenges still exist, because sensitive data of the vehicle user is necessary for generating a high-accuracy AI model. In this paper, we propose an authentication scheme to preserve the privacy of user data in edge intelligence-enabled VANETs. The proposed scheme can establish a secure communication channel using fuzzy extractor, elliptic curve cryptography (ECC), and physical unclonable function (PUF) technology. The proposed data upload process can provide privacy of the data using local differential privacy and symmetric key encryption. We validate the security robustness of the proposed scheme using informal analysis, the Real-Or-Random (ROR) model, and the Scyther tool. Moreover, we evaluate the computation and communication efficiency of the proposed and related schemes using Multiprecision Integer and Rational Arithmetic Cryptographic Library (MIRACL) software development kit (SDK). We simulate the practical deployment of the proposed scheme using network simulator 3 (NS-3). Our results show that the proposed scheme has a performance improvement of 10∼48% compared to the state-of-the-art research. Thus, we can demonstrate that the proposed scheme provides comprehensive and secure communication for data management in edge intelligence-enabled VANET environments.