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Collagen isolated from byproducts of common carp was hydrolyzed with alcalase enzyme to obtain peptide fractions. The resulting >30 kDa (PF1), 10–30 kDa (PF2), 3–10 kDa (PF3) and <1 kDa (PF4) fractions were studied for their antioxidant and functional properties. All peptide fractions illustrated antioxidant activity at different concentrations (1, 5, and 10 mg/mL). Although PF4 indicated the highest DPPH radical-scavenging activity (87%) at a concentration of 1 mg/mL, the highest reducing power (0.34) and hydroxyl radical scavenging activity (95.4%) were also observed in PF4 at a concentration of 10 mg/mL. The solubility of the peptide fractions was influenced by pH. The lowest solubility of the peptide fractions was observed at pH 4. The highest emulsifying activity index (EAI) was observed for PF4 (121.1 m2/g), followed by PF3 (99.6 m2/g), PF2 (89.5 m2/g) and PF1 (78.2 m2/g). In contrast to what has been found in the case of EAI, the emulsion stability of the peptide fractions decreased at lower molecular weight, which ranged from 24.4 to 31.6 min. Furthermore, it was revealed that PF1 had the highest foam capacity (87.4%) and foam stability (28.4 min), followed by PF2 and PF3. Overall, the findings suggest that peptide fractions isolated from byproducts of common carp are a promising source of natural antioxidants for application in functional food and pharmaceutical products.