The manner of storage of sugar beets largely influences their physical and chemical properties, which may subsequently determine their biochemical methane potential. In this study, samples of fresh sugar beets as well as beets stored in two ways—in airtight conditions and in an open-air container—were tested. In both cases, measurements were taken on specific dates, i.e., after 4, 8, 16 and 32 weeks of storage. A decrease in pH was observed in all samples, with the lowest decrease occurring in hermetically stored samples. The lowest pH value of 3.71 was obtained for sugar beets stored in an open-air container after 32 weeks of storage. During storage, a gradual decrease in total solids was also recorded along with accompanying losses of organic matter, more significant in the case of storage in an open-air container. In subsequent storage periods, the biogas/methane production efficiency differed slightly for both methods. The highest volume of biogas was obtained for fresh sugar beets—148.23 mL·g−1 fresh matter (FM)—and subsequently in the 8th and 16th weeks of storage: 139.35 mL·g−1 FM (H—airtight conditions) and 144.14 mL·g−1 FM (O—open-air container), and 147.58 H mL·g−1 FM (H) and 148.22 mL·g−1 FM (O), respectively. The storage period affected the time of anaerobic decomposition of the organic matter—fresh sugar beets took the longest to ferment (26 days), while the material stored for 32 weeks took the shortest to ferment. In the experiment, the content of selected organic compounds in individual samples, i.e., sugar, methanol, ethanol, lactic acid and acetic acid, was also analysed. Within these results, significant differences were found between the samples stored using the two different methods. A high content of sugar, methanol, ethanol and other chemical compounds in the “O” materials showed the hydrolysis and acidogenesis processes taking place in an open-air container, with the participation of catalytic microorganisms.