In the era of generative AI, ensuring the privacy of music data presents unique challenges: unlike static artworks such as images, music data is inherently temporal and multimodal, and it is sampled, transformed, and remixed at an unprecedented scale. These characteristics make its core vector embeddings, i.e, the numerical representations of the music, highly susceptible to being learned, misused, or even stolen by models without accessing the original audio files. Traditional methods like copyright licensing and digital watermarking offer limited protection for these abstract mathematical representations, thus necessitating a stronger, e.g., cryptographic, approach to safeguarding the embeddings themselves. Standard encryption schemes, such as AES, render data unintelligible for computation, making such searches impossible. While Fully Homomorphic Encryption (FHE) provides a plausible solution by allowing arbitrary computations on ciphertexts, its substantial performance overhead remains impractical for large-scale vector similarity searches. Given this trade-off, we propose a more practical approach using Additive Homomorphic Encryption (AHE) for vector similarity search. The primary contributions of this paper are threefold: we analyze threat models unique to music information retrieval systems; we provide a theoretical analysis and propose an efficient AHE-based solution through inner products of music embeddings to deliver privacy-preserving similarity search; and finally, we demonstrate the efficiency and practicality of the proposed approach through empirical evaluation and comparison to FHE schemes on real-world MP3 files.