Ab initio calculations have been used to investigate the interaction energies of dimers of dimethyl ether with benzene, hexafluorobenzene, and several monosubstituted benzenes. The potential energy curves were explored at the MP2/aug-cc-pVDZ level for two basic configurations of the dimers, one in which the oxygen atom of the dimethyl ether was pointed towards the aromatic ring and the other in which the oxygen atom was pointed away from the aromatic ring. Once the optimum intermolecular distances between the dimethyl and the aromatic ring had been determined for each of the dimers in both configurations at the MP2/aug-cc-pVDZ level, single point energy calculations were performed at the MP2/aug-cc-pVTZ level. A CCSD(T) correction term to the energy was determined and this was combined with the MP2/aug-cc-pVTZ energies to estimate the CCSD(T)/aug-cc-pVTZ interaction energies of the dimers. The estimated CCSD(T)/aug-cc-pVTZ interaction energies are predicted to be attractive for all of the dimers in both configurations and dispersion interactions are found to be a large component of the stabilization of the dimers. For the dimers with the dimethyl ether oxygen pointing towards the aromatic ring, the strengths of interaction energies are found to increase as the aromatic ring becomes more electron deficient, while for the dimers with the dimethyl ether oxygen pointing away from the aromatic ring, they increase as the aromatic ring becomes more electron rich. In both cases, the trends can be explained in terms of the electrostatic potentials of the dimethyl ether and the aromatic rings.