The effect of consuming baked foods enriched with antihypertensive compounds on blood pressure remains uncertain. In this study, an alcalase-generated amaranth hydrolyzate was used to prepare cookies and their technological characteristics (expansion factor, color, and texture) and antihypertensive properties evaluated. The bioavailability of the antihypertensive compounds were assessed in Balb/c mice and the antihypertensive effects in hypertensive rats. Enriched cookies developed a more intense yellow-brown color than the non-enriched ones (p < 0.05). Compared to the group that received water only, the sera of mice fed with enriched cookies significantly inhibited ACE-1 activity (p < 0.05). Similarly, enriched cookies, but not non-enriched ones, reduced the blood pressure in hypertensive rats (p < 0.05). Amaranth hydrolyzates maintain their antihypertensive properties after their incorporation into a cookie recipe and could be used as an ingredient for functional foods development.