The oxidation-reduction reactions of disulfides are important in both chemistry and biology. Dimethyl disulfide (DMDS), the smallest reduced sulfur species with a disulfide bond, is emitted in significant quantities from natural sources and contributes to the formation of aerosols and hazardous haze. Although atmospheric removal of DMDS via the reactions with OH or NO3 radicals and photolysis is known, the reactions of DMDS with other atmospheric oxidants are yet to be explored. Herein, using quantum chemical calculations, we explored the reactions of DMDS with CH2OO (formaldehyde oxide) and other methyl-substituted Criegee intermediates. The various reaction pathways evaluated were found to have positive energy barriers. However, in the presence of formic acid, a direct oxygen-transfer pathway leading to the corresponding sulfoxide (CH3SS(O)CH3) was found to proceed through a submerged transition state below the separated reactants. Calculations for the methyl-substituted Criegee intermediates, particularly for anti-CH3CHOO, show a significant increase in the rate of the direct oxygen-transfer reaction when catalyzed by formic acid. The presence of formic acid also alters the mechanism and reduces the enthalpic barrier of a second pathway, forming thioformaldehyde and hydroperoxide without any rate enhancement. Our data indicated that, although Criegee intermediates are unlikely to be an important atmospheric sink of DMDS under normal conditions, in regions rich in DMDS and formic acid, the formic acid-catalyzed Criegee intermediate-mediated oxidation of DMDS via the direct oxygen-transfer pathway could lead to organic sulfur compounds contributing to atmospheric aerosol.