The presence of opium alkaloids or pesticide residues in poppy seeds (Papaver somniferum L.) poses a potential health risk when consumed. Among the factors that could influence the levels of these substances in poppy seeds, the post-harvest cleaning plays a significant role. Thus, an analysis of 322 pesticide residues and 7 opium alkaloids in by-products of the mechanical cleaning of poppy seeds and in poppy seeds from a conventional Czech poppy production was conducted to evaluate this significance. Of the seven alkaloids tested, morphine was present in the highest concentration. Comparing the concentration of opium alkaloids determined in poppy samples, their levels were found to be approximately 100–1500 times higher in dried poppy capsules than in cleaned poppy seeds. With respect to pesticides, residues of five insecticides and nine fungicides were detected in poppy samples. In the case of pyrethroid insecticides and several triazole fungicides (difenoconazole, metconazole), post-harvest cleaning of poppy seeds appears to be highly efficient and results in residue levels in poppy seeds below the detection limit. A significant portion of the pesticide residues was present in the internal parts of the poppy seeds, as the pesticides were mostly systemic. The presence of opium alkaloids and pesticide residues on the surface of poppy seeds is due to external contamination by dust from crushed poppy seedpods. Therefore, proper post-harvest cleaning of poppy from dried poppy capsules seems to be an important tool to ensure the production of safe poppy seeds with lower contamination with alkaloids and several pesticide residues.