A comparative characterization of proteins from three edible insects—Tenebrio molitor (mealworm) larvae, Gryllus bimaculatus (cricket), and Bombyx mori (silkworm) pupae—was performed in this study. Proteins were extracted from edible insects and their hydrolysates were prepared through enzymatic hydrolysis with commercial enzymes (Flavourzyme: 12%; Alcalase: 3%). Solubility was significantly higher following enzymatic hydrolysis, while foamability was lower compared to those of the protein control. Angiotensin-converting enzyme was significantly inhibited after enzymatic hydrolysis, especially following Alcalase treatment, with IC50 values of 0.047, 0.066, and 0.065 mg/mL for G. bimaculatus, T. molitor larvae, and B. mori pupae, respectively. Moreover, the Alcalase-treated group of B. mori pupae and the T. molitor larvae group treated with a mixture of enzymes showed the effective inhibition of α-glucosidase activity. The anti-inflammatory activity of the insect hydrolysates was assessed via nitric oxide production from macrophages, and B. mori pupae samples exhibited significant activity regardless of the method of hydrolysis. These results indicate the functional properties of protein and hydrolysates from three species of edible insects, which may be useful in their future exploitation.