We report the first evidence of molecular gas in two atomic hydrogen (H i) clouds associated with gas outflowing from the Small Magellanic Cloud (SMC). We used the Atacama Pathfinder Experiment to detect and spatially resolve individual clumps of 12CO(2 → 1) emission in both clouds. CO clumps are compact (∼10 pc) and dynamically cold (line widths). Most CO emission appears to be offset from the peaks of the H i emission, some molecular gas lies in regions without a clear H i counterpart. We estimate a total molecular gas mass of in each cloud and molecular gas fractions up to 30% of the total cold gas mass (molecular + neutral). Under the assumption that this gas is escaping the galaxy, we calculated a cold gas outflow rate of and mass loading factors of at a distance larger than 1 kpc. These results show that relatively weak starburst-driven winds in dwarf galaxies like the SMC are able to accelerate significant amounts of cold and dense matter and inject it into the surrounding environment.