Sunflower meal (SM), a byproduct of sunflower seed oil extraction, contains approximately 30–50% proteins. Recognized for its high protein content and bioavailability, it is suitable for bioactive peptides production. Yet, research exploring the potential of sunflower proteins for generating metal-chelating peptides (MCPs) is sparse. Therefore, this study aimed to evaluate SM as a protein source to produce MCPs. After protein extraction to obtain a sunflower protein isolate, single and sequential enzymatic treatments were applied to produce hydrolysates using protamex (Prot) and protamex followed by Flavourzyme (Prot + Flav), respectively. Upon sequential treatment, effectively a large number of peptide bonds were cleaved, releasing mainly small-sized peptides. Prot hydrolysates exhibited the highest Fe2+-chelating properties, inhibition of Cu2+-induced reactive oxygen species (ROS) production, and ABTS scavenging activities. Besides, sequential hydrolysis with both enzymes enhanced the inhibition of Fe3+-induced ROS production and reducing power. The Cu2+-chelating peptides present in hydrolysates were separated by using immobilized metal ion affinity chromatography (IMAC-Cu2+) and identified by LC–MS/MS analysis. MS/MS analysis of enriched Cu2+-binding peptide fractions unveiled twenty-nine potential His-containing MCPs from SMPI hydrolysate. The molecular weight of Cu2+-identified peptides ranged from 0.8 to 1.7 kDa, with the larger-sized peptides (>kDa) presenting the most effective bioactive properties. His, Glu, and Asp residues were crucial for metal-chelating and antioxidant properties. Due to their high potential to bind Cu2+, Fe2+, and Fe3+, SM peptides could serve as potential MCP candidates for use as food or pharmaceutical agents to prevent metal-induced oxidation and related diseases.