The present study focuses on the impact of copper and silver nanoparticles on the chemical composition and physical properties of rapeseeds and rape sprouts. The seeds and sprouts were obtained from winter rape grown in a three-year cultivation (2018–2020) treated with silver (AgNP) and copper (CuNP) nanoparticles. In addition, the effect of the freeze-drying temperature (20; 40; 60 °C) on selected properties of the sprouts was studied. Spraying growing plants with nanoparticles resulted, in most cases, and depending on the year, in a reduction in the mass of seeds (MTS) by 9.5% (single nanoparticles spray ×1 CuNP in 2018), an increase in the fat content (by 8.80% for ×1 CuNP in 2018), a reduction in the protein content (by 12.93% for ×1 CuNP in 2018) and flavonoid content (by up to 58% for ×1 AgNP and CuNP in 2018), as well as increase in the glucosinolates content by 25% (for double nanoparticles spray ×2 AgNP in 2019). For the sprouts obtained from the rapeseeds, in most cases, a decrease in the content of flavonoids was observed (26.68% for ×1 AgNP; 20 °C in 2018), depending on the year of cultivation, the nanoparticles used, and the drying temperature. The obtained results remain inconclusive, which encourages the authors to undertake further research.