Certain post-harvest processes of medicinal and aromatic crops (MACs) such as washing, drying, cutting and milling, decontamination, packaging, and warehousing are widely applied in the industry. However, the effects of some of them on the active ingredients have been less thoroughly studied. Changes in the essential oil (EO) content and composition of hyssop leaves were studied under cold plasma treatments (voltage values of 17, 20 and 23 kV for 1, 5 and 10 min), using different packaging methods (packaged with air, nitrogen, and under vacuum) and storage duration (0, 3 and 6 months). All samples were hydro-distilled for EO content evaluation and EO composition was determined by gas chromatography and gas chromatography–mass spectrometry. In addition, color properties and structure of the glandular trichomes were studied. The results showed that cold plasma treatment significantly reduced EO content in comparison to the control, while higher intensities resulted in a greater reduction of EO. There were slight variations of a browning index between cold plasma treated samples, although no specific trend was observed. The trichomes were vulnerable to cold plasma intensity and prolongation. With increasing treatment duration at all intensities of cold plasma, important compounds such as cis-pinocamphone, trans-pinocamphone and β-pinene were reduced. The EO content was decreased with increasing storage time in all packaging methods, which was not significant in the samples packed with nitrogen gas. During the storage period, the amounts of cis and trans-pinocamphone were reduced, but β-pinene content increased. Overall, this study showed that the use of cold plasma as a new disinfection technique can cause changes in hyssop EO, while nitrogen packaging, compared to other methods, was able to preserve both EO content and components during storage.