The capacity of a millimeter wave propagation channel with multiple antennas is investigated focusing on the minimum antenna spacing required for taking a full advantage of multi-input multi-output (MIMO) systems. Especially, the effect of reflected paths is studied on the required minimum antenna spacing. A signal following a reflected path is assumed not to experience scattering which accompanies a random phase change. It is presented that MIMO channels with both line-of-sight and reflected paths enable a much smaller antenna spacing than those with only line-of-sight path. The required minimum antenna spacing for the former channels is seen to be an order of the wavelength or sometimes a fraction of the wavelength, while it should be at least a few tens of the wavelength for the latter.