The objective of this study was to investigate the biochemical antioxidant potential of peptides derived from enzymatically hydrolyzed mung bean (Vigna radiata) albumins using an 2,2′-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) radical scavenging assay, a ferrous ion chelating assay and an oxygen radical absorbance capacity (ORAC) assay. Peeled raw mung bean was ground into flour and mixed with buffer (pH 8.3, 1:20 w/v ratio) before being stirred, then filtered using 3 kDa and 30 kDa molecular weight cut-off (MWCO) centrifugal filters to obtain albumin fraction. The albumin fraction then underwent enzymatic hydrolysis using either gastrointestinal enzymes (pepsin and pancreatin) or thermolysin. Peptides in the hydrolysates were sequenced. The peptides showed low ABTS radical-scavenging activity (90–100 μg ascorbic acid equivalent/mL) but high ferrous ion chelating activity (1400–1500 μg EDTA equivalent/mL) and ORAC values (>120 μM Trolox equivalent). The ferrous ion chelating activity was enzyme- and hydrolysis time-dependent. For thermolysin hydrolysis, there was a drastic increase in ferrous ion chelating activity from t = 0 (886.9 μg EDTA equivalent/mL) to t = 5 min (1559.1 μg EDTA equivalent/mL) before plateauing. For pepsin–pancreatin hydrolysis, there was a drastic decrease from t = 0 (878.3 μg EDTA equivalent/mL) to t = 15 (138.0 μg EDTA equivalent/mL) after pepsin was added, but this increased from t = 0 (131.1 μg EDTA equivalent/mL) to t = 15 (1439.2 μg EDTA equivalent/mL) after pancreatin was added. There was no significant change in ABTS radical scavenging activity or ORAC values throughout different hydrolysis times for either the thermolysin or pepsin–pancreatin hydrolysis. Overall, mung bean hydrolysates produced peptides with high potential antioxidant capacity, being particularly effective ferrous ion chelators. Other antioxidant assays that use cellular lines should be performed to measure antioxidant capacity before animal and human studies.