Japanese knotweed (Fallopia japonica) and Bohemian knotweed (Fallopia × bohemica) are invasive plants that use allelopathy as an additional mechanism for colonization of the new habitat. Allelochemicals affect the growth of roots of neighboring plants. In the present study, we analyze the early changes associated with the inhibited root growth of radish seedlings exposed to aqueous extracts of knotweed rhizomes for 3 days. Here, we show that cells in the root cap treated with the knotweed extracts exhibited reduced cell length and displayed several ultrastructural changes, including the increased abundance of dilated ER cisternae filled with electron-dense material (ER bodies) and the accumulation of dense inclusions. Moreover, mitochondrial damage was exhibited in the root cap and the meristem zone compared to the non-treated radish seedlings. Furthermore, malfunction of the intracellular redox balance system was detected as the increased total antioxidative capacity. We also detected increased metacaspase-like proteolytic activities and, in the case of 10% extract of F. japonica, increased caspase-like proteolytic activities. These ultrastructural and biochemical effects could be the reason for the more than 60% shorter root length of treated radish seedlings compared to controls.