© 2013 IEEE.The rapid advance of manufacturing Unmanned Aerial Vehicles (UAVs, aka drones) has led to a rise in the use of their civilian and commercial applications. The access of these drones to controlled airspace can be efficiently coordinated through particular layered network architecture, often referred to as the Internet-of-Drones (IoD). The nature of IoD, which is deployed in an open-access environment, brings significant safety and security concerns. Classical cryptosystems such as elliptic curve cryptography, Rivest-Shamir-Adleman, and Diffie-Hellman are essential building blocks to secure communication in the IoD. However, with the rapid development of quantum computing, it will be easy to break public-key cryptosystems using efficient quantum algorithms like Shor's algorithm. Thus, building quantum-safe solutions to enhance IoD security has become imperative. Fortunately, quantum technologies can provide unconditional security solutions to protect data and communications in the IoD environment. This paper proposes a quantum-based scheme to prevent unauthorized drones from accessing a specific flight zone and authenticates the identities and shared secret messages of involved entities. To do so, we used a quantum channel to encode the private information based on a pre-shared key and a random key generated in a session. The involved entities also perform mutual authentication and share a secret key. We also provide the security proofs and analysis of the proposed scheme that indicates its resistance to well-known attacks.