Rosmarinus officinalis L. (rosemary) is a medicinal plant that is native to the Mediterranean region and is grown worldwide. In addition to being used therapeutically, it is frequently used as a condiment and food preservative. In addition to its significance in the food industry, rosemary essential oil (EO) is used worldwide to cure a wide range of maladies, including respiratory, gastrointestinal, and inflammation-related problems. Therefore, how this plant is stored is crucial. This study examined the multiple effects of packaging materials, storage period, and their interactions on the quantity and chemical components of rosemary EO. The net results revealed that these factors caused a decrease in the amount of extracted oil during the storage period (2−4 months). The results of GC-MS and the chemometric analysis, including principal component analysis (PCA) and agglomerative hierarchical clustering (AHC), revealed that the concentrations of the main compounds, including camphor, α-pinene, eucalyptol, camphene, and D-limonene, varied from 18.87%–30.31%, 14.09%–19.40%, 15.82%–17.56%, 3.36%–6.06%, and 4.82%–8.31%, respectively, in the EOs of all the different treatments. Additionally, the results showed that polypropylene and linen bags are the best bags for saving the rosemary plants without significant variations compared to those of rosemary plants before storage.