Yersiniosis, one of the leading foodborne infections in the European Union, is caused by Yersinia enterocolitica. In this study, the antibacterial and antibiofilm effects of cinnamon (Cinnamomum zeylanicum Nees), clove (Syzygium aromaticum L.), oregano (Origanum vulgare L.), rosemary (Rosmarinus officinalis L.), thyme (Thymus vulgaris L.), and winter savory (Satureja montana L.) essential oils were investigated against Y. enterocolitica strains belonging to the bioserotype 4/O:3. Cinnamon essential oil showed the highest antibacterial activity, with an MIC value 0.09 µL/mL, followed by oregano and thyme essential oils, with MIC values from 0.09 to 0.18 µL/mL, and from 0.18 to 0.23 µL/mL, respectively. Thyme essential oil at 0.23 µL/g (MIC) and at 0.46 µL/g (2MIC) significantly (p < 0.05) reduced the number of Y. enterocolitica by 0.38 log CFU/g and 0.64 log CFU/g, respectively, in minced pork meat during storage at 4 °C for 4 days. The Y. enterocolitica strains formed biofilms at 15 °C and 37 °C in tryptic soy broth and Luria–Bertani broth, while no biofilms were obtained at 5 °C, and in meat broth nutrient media. Applying the minimum bactericidal concentrations of cinnamon, clove, oregano, rosemary, thyme, and winter savory essential oils on preformed biofilms led to significant reductions being observed in the range from 45.34% to 78.89%. A scanning electron microscopy assay showed the devastating impact of oregano and thyme essential oils on the morphology of Y. enterocolitica bacterial cells. In conclusion, the results of this study show that essential oils possess high anti-Yersinia and antibiofilm effects.