Mobile social networks (MSNs) enable mobile users to connect, communicate, and share content primarily through mobile devices with other individuals. Profile matching is a crucial service in MSNs, allowing users to select individuals with similar profile attributes. However, the unintended disclosure of user profile information to MSN service providers and other users raises significant concerns regarding security and privacy. Although many proposals have been introduced to address these issues, they overlook the threats posed by powerful quantum computers, resulting in potential vulnerabilities in existing solutions. In this paper, we propose a quantum-secure fine-grained privacy-preserving profile matching (QF2PM) scheme for MSNs, which supports finer differentiation among users with similar attributes. Our scheme enables the initiator and candidate to share a secret key with the help of a semi-honest quantum server. We employ rotational encryption and multi-qubit swap tests to achieve profile matching while preventing privacy leakage, even in the face of future quantum threats. In contrast to existing privacy-preserving profile matching schemes, our proposal can withstand both classical and quantum attacks, leveraging quantum technologies such as Bell states, rotational encryption, multi-qubit swap test, and quantum measurement.