Pterygoplichthys disjunctivus, locally named the armoured catfish, is a by-catch of tilapia fishing that accounts for up to 80% of total captured fish in the Adolfo Lopez Mateos dam, in Michoacán, México, affecting the economy of its surrounding communities. This invasive fish is discarded by fishermen since native people do not consume it, partly due to its appearance, yet it is rich in protein. The aim of this study was to produce hydrolysates from armoured catfish using food-grade proteases (neutrases HT and PF and alcalase PAL) and investigate the processing conditions (pH and temperature) that lead to a high degree of hydrolysis, antioxidant activity, and Angiotensin I-Converting Enzyme (ACE) Inhibitory activity. No other similar research has been reported on this underutilized fish. The antioxidant activity was measured by three different methods, ABTS, FRAP and ORAC, with relevance to food and biological systems in order to obtain a more comprehensive assessment of the activity. In addition, the main peptide sequences were identified. All enzymes produced hydrolysates with high antioxidant activity. In particular, the protease HT led to the highest antioxidant activity according to the ABTS (174.68 μmol Trolox equivalent/g fish) and FRAP (7.59 mg ascorbic acid equivalent/g fish) methods and almost the same as PAL according to the ORAC method (51.43 μmol Trolox equivalent/g fish). Moreover, maximum activity was obtained at mild pH and temperature (7.5; 50 °C). Interestingly, the ORAC values obtained here were higher than others previously reported for fish hydrolysates and similar to those reported for fruits such as blueberries, apples and oranges. The peptide sequence IEE(E) was present in several peptides in both hydrolysates; this sequence may be partly responsible for the high antioxidant activity, particularly the one based on iron-reducing power. These findings will be relevant to the valorization of other fish/fish muscle discards and could contribute to the production of food supplements and nutraceuticals.