Protein hydrolysates with 20% and 30% degrees of hydrolysis (DH) were produced from alcalase hydrolysis of Pacific white shrimp shells. The study aimed to investigate the antioxidant and antihypertensive activities of these protein hydrolysates, focusing on peptide fractions of various molecular weights (MW) obtained through ultrafiltration. The 30% DH protein hydrolysate (SSPH) showed the highest antioxidant activities and was subjected to ultrafiltration to produce peptides of various molecular weights (MW) (F1:10–50, F2:5–10, F3:3–5, F4:1-3, and F5:<1 kDa). SSPH showed higher hydrophilic and non-essential amino acid content, among which alanine and aspartic acid were at higher levels. The obtained peptide fractions were analyzed for various antioxidant activities and inhibitory activities against angiotensin-converting enzyme and renin. F4 and F2 samples showed the highest DPPH (2.00 mM TE/g sample) and ABTS (60.68 mM TE/g sample) radical scavenging activities, respectively. Superoxide and hydrogen peroxide radical scavenging activity augmented with decreasing MW, aside from for F1, which showed higher activity than F2–F4 (p < 0.05). The highest ACE-inhibitory activity was found for the F2 fraction (44%–55%), and renin inhibitory activity increased with decreasing MW, in which F5 (12%–22%) was the most effective (p < 0.05). F5 showed 6 major peptides, among which KLVRGSKS and LPKKCLSARPG were the dominant sequences. Thus, this study suggests that shrimp shell protein isolate could be an alternative protein source for peptides with various antioxidant and antihypertensive activities, with potential applications in functional foods and nutraceuticals aimed at mitigating oxidative stress and hypertension.