The production of Red Jonaprince cultivar is increasing, but the quality of apples is still challenging. Therefore, various options may be used including 1-Methylcyclopropene (1-MCP) application, as it influences ethylene receptors and blocks them, resulting in the possibility of delaying harvesting. The preharvest application of 1-MCP has not been studied so far for this cultivar but for other ones it has been successful, as it is based on the understanding of the natural apple ripening process. The study aimed to analyze the possibility of applying a 1-MCP treatment in the preharvest period for Red Jonaprince apples. The study was conducted based on a comparison of apples from two groups of Red Jonaprince apple trees (4 years) cultivated in an experimental orchard, where for one of them 1-MCP was applied in the preharvest period (HarvistaTM; 150 g per ha; 20 September—12 days before the optimum harvesting window (OHW)). For both groups, the apples were studied twice, for harvesting in the OHW (2 October) and for delayed harvesting (24 October). The harvested fruits were stored in an Ultra Low Oxygen chamber (ULO; 1.2% CO2, 1.2% O2) until May. They were analyzed before storage (preharvest) five times (20 September–24 October) and after storage (postharvest) three times (20 March–18 May). The following parameters were included: firmness, total soluble solids (TSS) content, titratable acidity (TA). For the preharvest period, the parameters also included internal ethylene content (IEC), starch index, and Streif index. For the preharvest period, significant differences associated with the 1-MCP treatment (p ≤ 0.05) were observed for the IEC (lower results for apples treated for 4th and 5th assessment), TA (higher results), and Streif index (higher results). Meanwhile, for firmness, TSS, and starch index for the majority of measurements there were no differences (p > 0.05). For the postharvest period, significant differences associated with 1-MCP treatment (p ≤ 0.05) were observed for firmness (higher results) and TA (higher results) both for OHW and delayed harvesting. It was concluded that a preharvest 1-MCP treatment allowed delayed harvesting and reduced the quality deterioration during the ULO storage of Red Jonaprince apples.