Cassava has the potential to alleviate food insecurity in many tropical regions, yet few breeding efforts to increase yield have been made. Improved photosynthetic efficiency in cassava has the potential to increase yields, but cassava roots must have sufficient sink strength to prevent carbohydrates from accumulating in leaf tissue and suppressing photosynthesis. Here, we grew eight farmer-preferred African cassava cultivars under free-air CO2 enrichment (FACE) to evaluate the sink strength of cassava roots when photosynthesis increases due to elevated CO2 concentrations ([CO2]). Relative to the ambient treatments, elevated [CO2] treatments increased fresh (+27%) and dry (+37%) root biomass, which was driven by an increase in photosynthesis (+31%) and the absence of photosynthetic down-regulation over the growing season. Moreover, intrinsic water use efficiency improved under elevated [CO2] conditions, while leaf protein content and leaf and root cyanide concentrations were not affected. Overall, these results suggest that higher cassava yields can be expected as atmospheric [CO2] increases over the coming decades. However, there were cultivar differences in the partitioning of resources to roots versus above-grown biomass; thus, the particular responses of each cultivar must be considered when selecting candidates for improvement.