Heavy metal-polluted soil represents an important stress condition for plants. Several studies demonstrated that growth inhibition under metal stress and metal-induced damages, including genotoxicity, is particularly pronounced at the early stages of seedling growth. Moreover, it is reported that heavy metals enter the cytoplasm to exert their detrimental effect, including DNA damage. In this work, we estimated (i) metal-induced genotoxicity by ISSR molecular markers and (ii) the distribution of the metal fractions between symplast and apoplast by EDTA washing, in three cultivars of Cynara cardunculus var. altilis (L.) DC (Sardo, Siciliano, and Spagnolo), grown in hydroponics for 15 days with Cd or Pb: In line with the literature, in all cultivars, the genotoxic damage induced by Pb was more severe compared to Cd. However, a cultivar-specific response was evidenced since Spagnolo showed, under metal stress, a significantly higher genome template stability compared to the other examined cultivars. The lower genotoxicity observed in Spagnolo could depend on the lower intracellular metal concentration measured in this cultivar by chemical analysis. Accordingly, light microscopy highlighted that Spagnolo developed smaller and more numerous epidermal cells under metal stress; these cells would provide a larger wall surface offering a wider metal sequestration compartment in the apoplast.