We conduct a systematic numerical study of passive scalar structures in supersonic turbulent flows. We find that the degree of intermittency in the scalar structures increases only slightly as the flow changes from transonic to highly supersonic, while the velocity structures become significantly more intermittent. This difference is due to the absence of shocklike discontinuities in the scalar field. The structure functions of the scalar field are well described by the intermittency model of She and Lévêque [Phys. Rev. Lett 72, 336 (1994)], and the most intense scalar structures are found to be sheetlike at all Mach numbers.