‘Red Jonaprince’ cultivar production is rapidly increasing; therefore, the interest in harvesting in various regions, as well as in improving and maintaining the quality of the apple, is also increasing. The aim of this study was to analyze the possibility of applying 1-MCP treatment in pre- and postharvest treatment for ‘Red Jonaprince’ apples for maintaining the quality of the apple after Ultra-Low Oxygen (ULO) storage. The studied apples were assessed in four groups: 0—control group without any specific treatment applied; group 1—1-MCP applied preharvest; group 2—1-MCP applied postharvest; group 3—1-MCP applied preharvest and postharvest. Measurements were conducted directly after 3, 5 and 6 months of ULO storage and additionally after 7 days of simulated distribution for each period of storage. The 24 groups obtained (four treatments × three storage periods × two simulated distribution periods) were evaluated for firmness, soluble solids content (SSC) and titratable acidity (TA). No statistically significant impact on the SSC of ‘Red Jonaprince’ for all groups was stated (p > 0.05), while for the firmness and TA values, there was a statistically significant impact of applied treatment (ULO storage period and simulated distribution) (p < 0.05). Longer ULO storage as well as longer simulated distribution were associated with decreasing firmness and decreasing TA of apples (p < 0.05). For samples subjected to 1-MCP treatment postharvest and those subjected to 1-MCP treatment preharvest and postharvest combined, the apples in the majority of analyses were protected against decreasing firmness and decreasing TA. It may be concluded that postharvest 1-MCP treatment applied for ‘Red Jonaprince’ apples allows maintaining its quality parameters, including firmness and TA of fruits. Taking this into account, our recommendation is that the postharvest 1-MCP treatment should be sufficient, in order to avoid unreasonable management of 1-MCP, which is not justified to be applied preharvest, or preharvest and postharvest combined, for ‘Red Jonaprince’ apples.