Heavy metals are environmental pollutants that cause toxicity in plants and represent a risk for human health, linked to bioaccumulation through the food chain. However, excess accumulation may not occur in young plants in the early stages of exposure to the toxic element. In the present work, rocket (Eruca sativa L.) plants grown in hydroponics were exposed for three weeks to excess concentrations (25, 50, or 100 µM) of Cu or Zn in the nutrient solution and were more sensitive to Cu than Zn toxicity. However, a significant decrease in the leaf biomass production as compared with the control was observed only after two or three weeks, and only minor signals of metal-induced adverse effects were evidenced concerning photosynthesis, oxidative stress indicators, antioxidant metabolites, and macronutrients. After two or three weeks, the leaf level of Cu occasionally approached the upper value associated with the recommended limits of dietary intake for human adults. However, as rocket leaves are commercialized when they achieve a 10–15 cm length, after one week of cultivation in perlite, the plants had an adequate size without metal contamination and could be considered suitable for the food market, even after exposure to Cu or Zn concentrations up to 100 µM.