The free jet millimeter-wave absorption spectra of two isotopomers of the weakly bonded dimethyl ether-Kr complex have been assigned and measured. The Kr atom lies in the sigma(v) symmetry plane of dimethyl ether perpendicular to the COC plane, at a r(0)-distance of 3.67 Angstrom from its center of mass (cm). The line connecting the krypton atom to cm forms an r(0)-angle of 70degrees with the O-cm line. The observed conformation is in agreement with the global minimum as found with a distributed polarizability model. Many rotational transitions are split into two component lines, due to the motion of Kr relative to dimethyl ether in the complex. The corresponding splitting has been used to determine the barrier to the internal motion. Information on the dissociation energy has been deduced from the centrifugal distortion effects.