The aim of this work was to characterize the antioxidant properties of some of the peptides present in bromelain mung bean meal protein hydrolysate (MMPH). The MMPH was subjected to two rounds of bioassay-guided reversed-phase HPLC separation followed by peptide identification in the most potent fractions using tandem mass spectrometry. Twelve antioxidant peptides, namely, HC, CGN, LAN, CTN, LAF, CSGD, MMGW, QFAAD, ERF, EYW, FLQL, and QFAW were identified and assayed for antioxidant properties. CTN, HC, CGN, and CSGD were the most potent (p < 0.05) DPPH radical scavengers with EC50 values of 0.30, 0.29, 0.28, and 0.30 mg/mL, respectively, which are lower than the 0.03 mg/mL obtained for reduced glutathione (GSH). CTN, HC, CGN, and CSGD exhibited the most potent (p < 0.05) scavenging activities against hydroxyl and superoxide radicals with EC50 values that are similar to those of GSH. The cysteine-containing peptides also had stronger ferric reducing antioxidant power and metal chelation activity than peptides devoid of cysteine. In contrast, MMGW, ERF, and EYW had poor radical scavenging and metal chelation activities. We conclude that the availability of the sulfhydryl group may have enhanced antioxidant potency while the presence of bulky groups such phenylalanine and tryptophan had an opposite effect.