First there is different kinds of MBPs. But usually there is hydrogen bonding, but also aromatic residues, and particularly Trp, which are creating platforms / hydrophobic stacking which are particularly important.
When dealing whith such kinds of questions, do not hesitate to look into pdb and/or Cazypedia.
There are also many types of maltose-related ligands but as in the case of different types of MBP's the binding is by hydrogen bonding and non-polar interaction with the aromatic side chain (electron clouds) within the binding pocket. One or both type of interactions predominate depending upon the type of maltose ligand and culminating in the ligand being/not being transported from the periplasm (of E. coli for example). There are a couple of domains that make up the binding pocket and each has its respective aromatic and hydrogen-bonding residues. This mechanism is not necessarily related to MBP's supposed ability to confer increased solubility to the fusion protein but it is related to the type of ligand used for MBP affinity capture/release which in turn may be relevant to your purification plans.