We investigate the structure and kinematics of the circumstellar disk around the Herbig Ae star MWC 758 using high resolution observations of the 12CO (3-2) and dust continuum emission at the wavelengths of 0.87 and 3.3 mm. We find that the dust emission peaks at an orbital radius of about 100 AU, while the CO intensity has a central peak coincident with the position of the star. The CO emission is in agreement with a disk in keplerian rotation around a 2.0 Msun star, confirming that MWC758 is indeed an intermediate mass star. By comparing the observation with theoretical disk models, we derive that the disk surface density Sigma(r) steeply increases from 40 to 100 AU, and decreases exponentially outward. Within 40 AU, the disk has to be optically thin in the continuum emission at millimeter wavelengths to explain the observed dust morphology, though our observations lack the angular resolution and sensitivity required to constrain the surface density on these spatial scales. The surface density distribution in MWC 758 disk is similar to that of ``transition disks, though no disk clearing has been previously inferred from the analysis of the spectral energy distribution (SED). Moreover, the asymmetries observed in the dust and CO emission suggest that the disk may be gravitationally perturbed by a low mass companion orbiting within a radius of 30 AU. Our results emphasize that SEDs alone do not provide a complete picture of disk structure and that high resolution millimeter-wave images are essential to reveal the structure of the cool disk mid plane.