Copper (Cu)-contaminated soils are becoming more common, and phytoremediation is an effective strategy for reducing the negative effects of Cu on soils. Tree species are commonly used for this technique because they act as a barrier to this type of contamination. It is necessary to evaluate Cu tolerance and toxicity thresholds together with the harm this metal causes to plants. The objective of the current study was to investigate the tolerance of Handroanthus heptaphyllus plants to Cu through morpho-physiological, biochemical, and tissue Cu concentration analyses. H. heptaphyllus seedlings were subjected to nutrient solutions with varying concentrations of copper: 0, 5, 32, 64, 96, and 128 µM Cu in a hydroponic system. We conducted a morpho-physiological trait analysis on shoot height, root length, dry weight, morphological variables of the root system, leaf area, and photosynthetic variables. In addition, we also looked into photosynthetic pigments, antioxidant enzymes, lipid peroxidation, hydrogen peroxide concentration, and Cu accumulation in tissues. The values obtained for variables such as dry weight and pigments did not show significant differences, regardless of Cu concentration. Moreover, photosynthetic and transpiration rates were negatively affected only at the highest Cu concentration (128 µM). Overall, excess Cu had no effect on Handroanthus heptaphyllus below 128 µM. Cu accumulated mainly in the roots without a decrease in biomass, which could indicate the tolerance of the species to this metal as well as its great potential in the phytostabilization of Cu in contaminated soils.