Cross-linked enzyme crystals (CLECs) enclose an extensive regular matrix of chiral solvent-filled nanopores, via which ions and solutes travel in and out. Several cross-linked enzyme crystals have recently been used for chiral separation and as biocatalysts. We studied the dynamics of solute transport in orthorhombic d-xylose isomerase (XI) crystals by means of Brownian dynamics (BD) and molecular dynamics (MD) simulations, which show how the protein residues influence the dynamics of solute molecules in confined regions inside the lattice. In the BD simulations, coarse-grained beads represent solutes of different sizes. The diffusion of S-phenylglycine molecules inside XI crystals is investigated by long-time MD simulations. The computed diffusion coefficients within a crystal are found to be orders of magnitude lower than in bulk water. The simulation results are compared to the recent experimental studies of diffusion and reaction inside XI crystals. The insights obtained from simulations allow us to understand the nature of solute-protein interactions and transport phenomena in CLECs, which is useful for the design of novel nanoporous biocatalysts and bioseparations based on CLECs.