Moringa oleifera L. is greatly appreciated for its high content of phytochemicals. Although most parts of moringa tree have been widely studied, seeds remained scarcely explored. The first goal of this study was to investigate the effectiveness of germination to improve the nutritional composition (proximate composition and levels of vitamins B1 and B2), content of bioactive compounds (glucosinolates, phenolics and γ-aminobutyric acid, GABA) and antioxidant activity of moringa seed. Germination improved protein, fat, fiber, riboflavin, phenolics, some individual glucosinolates (GLS) and GABA contents, as well as the antioxidant potential in moringa sprouts, but the extent of the improvement depended on germination conditions. The second objective of this work was to identify the optimal germination conditions to maximize nutritional and bioactive quality of moringa by applying multi-response optimization (response surface methodology, RSM). RSM models indicated that 28 °C and 24 h were the optimal conditions to enhance the accumulation of riboflavin, phenolics and antioxidant activity of sprouts, while the highest GABA and total GLS contents were observed at 36 °C for 96 h and thiamine achieved the maximum content at 36 °C for 24 h. These results show that moringa sprouts are promising functional foods that might be also used as ingredients for the elaboration of novel foodstuffs.