This study aimed to encapsulate Foeniculum vulgare and Carum carvi essential oils (FVO and CCO) into the zein (ZN) nanofibers using an electrospinning technique and examine their application in retarding the growth of bacterial pathogens in ground beef meat during refrigerated storage conditions. The main fractions of FVO included trans-anethole (37.98%), α-fellandrene (15.09%), fenchone (10.58%), and tarragon (7.58%). CCO's major chemical compositions were also identified as α-terpinene (19.67%), α-terpinene-7-al (18.86%), p-menthatriene (16.90%), and cuminaldehyde (15.96%). The Fourier transform infrared spectroscopy analysis verified the molecular interaction between FVO/CCO and the ZN polymer. The thickness, tensile strength, elongation at break, and water vapor permeability of the nanofiber mats were in the range of 0.20–0.22 mm, 6.01–9.22 MPa, 5.57%–10.78%, and 1.05–2.72 × 10‾14 kg m/m2 s Pa, respectively. The initial count of 5 log CFU/g of Staphylococcus aureus, Listeria monocytogenes, and Yersinia enterocolitica in ground beef meat packaged with ZN + FVO 1 mL/100 mL + CCO 1 mL/100 mL nanofiber mats, as the best group, reached <1.00, 2.52, and 3.13 log CFU/g, respectively, at the end of the study (day 10), suggesting that the designated nanofiber mats can be utilized for antimicrobial food packaging applications.