In this work, we evaluated the physical and oxidative stabilities of 5% w/w fish oil-in-water emulsions stabilized with 1%wt Tween20 and containing 2 mg/mL of protein hydrolysates from olive seed (OSM–H), sunflower (SFSM–H), rapeseed (RSM–H) and lupin (LUM–H) meals. To this end, the plant-based substrates were hydrolyzed at a 20% degree of hydrolysis (DH) employing a mixture 1:1 of subtilisin: trypsin. The hydrolysates were characterized in terms of molecular weight profile and in vitro antioxidant activities (i.e., DPPH scavenging and ferrous ion chelation). After incorporation of the plant protein hydrolysates as water-soluble antioxidants in the emulsions, a 14-day storage study was conducted to evaluate both the physical (i.e., ζ-potential, droplet size and emulsion stability index) and oxidative (e.g., peroxide and anisidine value) stabilities. The highest in vitro DPPH scavenging and iron (II)-chelating activities were exhibited by SFSM–H (IC50 = 0.05 ± 0.01 mg/mL) and RSM–H (IC50 = 0.41 ± 0.06 mg/mL). All the emulsions were physically stable within the storage period, with ζ-potential values below −35 mV and an average mean diameter D[4,3] of 0.411 ± 0.010 μm. Although LUM–H did not prevent lipid oxidation in emulsions, OSM–H and SFSM–H exhibited a remarkable ability to retard the formation of primary and secondary lipid oxidation products during storage when compared with the control emulsion without antioxidants. Overall, our findings show that plant-based enzymatic hydrolysates are an interesting alternative to be employed as natural antioxidants to retard lipid oxidation in food emulsions.