The advent of 6G communication introduces extreme performance requirements, including sub-millisecond latency, high reliability, and massive connectivity. These demands, combined with the threat posed by quantum computers, render classical cryptographic schemes such as RSA-2048 and ECC-P256 insecure. This paper presents a lattice-based post-quantum cryptographic (PQC) framework designed to secure 6G networks against quantum attacks. The proposed approach employs Module-LWE–based key encapsulation mechanisms and digital signatures. Numerical analysis demonstrates that the proposed lattice-KEM requires approximately 1184 bytes of public key and 1088 bytes of ciphertext, compared to 256 bytes for RSA-2048 and 64 bytes for ECC-P256. Computation time for lattice operations is measured at 148 ms, while RSA and ECC require 63 ms and 1.6 ms, respectively. Simulation results further show that at a 50-kbps control-channel rate, lattice-based key establishment incurs ~320 ms latency, whereas RSA and ECC require 102 ms and 11 ms. Despite higher communication overhead, the proposed method achieves 256-bit quantum security, outperforming classical systems vulnerable to quantum attacks. These findings confirm the suitability of lattice-based PQC as a robust and future-proof security solution for 6G networks.