Multi-designated verifier ring signatures (MDVRS) are an anonymous signature primitive proposed by Kolby et al. (IACR CIC 2024) in which only designated verifiers can verify signatures. They formalized MDVRS and constructed an MDVRS scheme through a specific intermediate primitive, named provably simulatable designated-verifier ring signatures (PSDVRS). However, PSDVRS is only known from the discrete logarithm assumption. In this paper, we propose a new generic construction of MDVRS from widely-known primitives, public key encryption schemes, one-time signatures, ring signatures, and non-interactive zero-knowledge arguments. As these building blocks can be constructed from various computational assumptions, we can realize MDVRS from them. Namely, we obtain post-quantum MDVRS for the first time. Furthermore, our generic construction achieves stronger security than the original scheme.