Dill (Anethum graveolens L.) essential oil (DEO) obtained by hydrodistillation (HD) and lipid extracts (DSE₁ and DSE₂) obtained by supercritical CO₂ extraction (SFE) were used as potential antioxidants and antimicrobial agents in beef burgers at two different concentrations (0.075 and 0.15 µL/g). The chemical profile of the lipid extracts and their in vitro antimicrobial activity against the common pathogens E. coli and L. monocytogenes (MIC and MBC) were determined. The quality and shelf life of the burgers were monitored through (lipid oxidation—TBARS test; protein oxidation—thiol group content and selected biogenic amine content) and microbiological quality (Enterobacteriaceae—EB, aerobic mesophilic bacteria—TAMB, lactic acid bacteria—LAB). Dill lipid extracts (DEO and DSE₁) significantly (p < 0.05) reduced lipid oxidation and protein oxidation in beef burgers, while the lipid extract (DSE₂) showed pro-oxidative effects. The strongest antimicrobial potential against EB was found in SFE₁150 (1.15 log cfu/g). Putrescine, cadaverine, histamine, and tyramine were not detected in any of the analyzed samples during the storage period, while the total content of biogenic amines ranged from 21.4 mg/kg to 285 mg/kg. Generally, it can be concluded that dill essential oil (DEO) and extract DSE₁ can be used as novel natural additives in minced-meat products.