An undeniable signature scheme is type of digital signature where the signer retains control over the signature's verifiability. Therefore with the approval of the signer, only an authenticated verifier can verify the signature. In this work, we develop a module lattice-based post-quantum undeniable signature system. Our method is based on the GPV framework utilizing module lattices, with the security assured by the hardness of the SIS and LWE problems. We have thoroughly proved all the desired securities for the proposed scheme. Finally, we have implemented our protocol for different sets of parameters. The purpose of opting a module variant rather than a ring variant is to provide greater flexibility in selecting parameters.