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We report a hybrid parallel central and graphics processing units (CPU-GPU) implementation of a coarse-grained model for replica exchange Monte Carlo (REMC) simulations of protein assemblies. We describe the design, optimization, validation, and benchmarking of our algorithms, particularly the parallelization strategy, which is specific to the requirements of GPU hardware. Performance evaluation of our hybrid implementation shows scaled speedup as compared to a single-core CPU; reference simulations of small 100 residue proteins have a modest speedup of 4, while large simulations with thousands of residues are up to 1400 times faster. Importantly, the combination of coarse-grained models with highly parallel GPU hardware vastly increases the length- and time-scales accessible for protein simulation, making it possible to simulate much larger systems of interacting proteins than have previously been attempted. As a first step toward the simulation of the assembly of an entire viral capsid, we have demonstrated that the chosen coarse-grained model, together with REMC sampling, is capable of identifying the correctly bound structure, for a pair of fragments from the human hepatitis B virus capsid. Our parallel solution can easily be generalized to other interaction functions and other types of macromolecules and has implications for the parallelization of similar N-body problems that require random access lookups.