Chickpea (Cicer arietinum L.) peptides have shown in vitro potential to inhibit the angiotensin I-converting enzyme (ACE-I). However, the potential molecular interactions between chickpea peptides (CP) and ACE-I as well as their ADMET (absorption/distribution/metabolism/excretion/toxicity) characteristics remain unknown. Thus, our aim was to study the in silico interactions of CP with ACE-I and the CP ADMET characteristics. Legumin and provicilin sequences were submitted to in silico analysis to search for ACE-I inhibitory peptides. Simulated enzymatic hydrolysis was performed using the BIOPEP-UWM database, and the ACE-I inhibitory peptides generated (EC50 ≤ 200 μM) were selected to perform molecular docking and ADMET analysis. After hydrolysis, 59 out of 381 peptides with ACE-I inhibitory potential were released. Based on A and B parameters, the legumin peptides showed better ACE-I inhibitory potential than the provicilin ones. CP mainly interact with residues from pocket S1 (Ala354/Glu384) and S2 (His353/His513) through hydrogen bonds (distances < 3.0 Å) and hydrophobic interactions (binding energy from −5.7 to −9.2 kcal/mol). Through ADMET analysis, CP showed optimal values for inhibiting ACE-I in vivo. ACE-I inhibitory peptides from legumin and provicilin can bind strongly and tightly to the active site of ACE-I. Further studies to evaluate in vivo the antihypertensive effects of CP are warranted.