The aim of this work is to establish the most suitable proteolysis conditions to obtain bovine casein hydrolysates containing peptides with antioxidant and antihypertensive capacity. To this end, the proteolytic activity of Cynara scolymus L. flower extracts was characterized on whole bovine casein, evaluating the effect of several factors (pH, temperature, substrate concentration, enzyme concentration, and hydrolysis time). The optimal conditions to carry out the hydrolysis with the C. scolymus L. extract were as follows: pH 6.2, 50 °C, and 0.023 mg·mL−1 of extract-protein concentration. A Michaelis constant (Km) value of 5.66 mg·mL−1 and a maximum rate of reaction (Vmax) of 8.47 mUAbs∙min−1 were observed. The optimal hydrolysis time was 17 h. The casein hydrolysates obtained with these conditions contained peptides with antioxidant activity (1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging capacity: 30.89%; Trolox equivalent antioxidant capacity (TEAC) against 2,2’-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) free radical (ABTS●+): 4.43 mM Trolox equivalent·mg−1 peptide) and antihypertensive activity, showing 55.05% angiotensin-converting enzyme-I inhibition in vitro.