Enzymatic pea protein hydrolysates offer potential health benefits because of their content of bioactive peptides, which have been released from the protein by the action of proteases. This study examined how the degree of hydrolysis (DH) of pea protein with trypsin influences physicochemical parameters and antioxidant capacity of the resulting hydrolysates. The molecular weight (MW) distribution of a pea protein isolate and its hydrolysates at the DHs of 2%, 5%, 8%, and 12% was determined using size-exclusion chromatography. Surface hydrophobicity was evaluated by two fluorescent probe assays, namely 8-anilino-1-naphthalenesulfonic acid (ANS) and cis-parinaric acid (CPA). Antioxidant potential was assessed as ABTS•+ scavenging capacity, oxygen radical absorbance capacity (ORACFL), antioxidant capacity of water-soluble and lipid-soluble compounds in the photochemiluminescence assay (PCL-ACW and PCL-ACL, respectively), and the ability to inhibit the oxidation of β-carotene-linoleic acid emulsion. With increasing DH, the contribution of fractions with MWs of 2–4 kDa and 4–7 kDa in the hydrolysates increased. However, the relative content of peptides with MWs less than 2 kDa remained below 10% in all of them. The ABTS•+ scavenging capacity and ORACFL also increased with DH, and the highest values, 0.111 and 0.320 mmol Trolox equivalent/g, respectively, were obtained for the hydrolysate at a DH 12%. Surface hydrophobicity increased only to DH 5%. Hydrolysates at DHs of 8% and 12% were characterized by gradually lower values. The trend of surface hydrophobicity changes was consistent with that of PCL-ACL. Additionally, principal component analysis showed an association between surface hydrophobicity and antioxidant capacity in the model emulsion. Overall, tryptic pea protein hydrolysates had improved antioxidant properties compared to the isolate, and the degree of hydrolysis was a parameter that allowed optimizing these properties under different conditions of antioxidant action.