A comprehensive study of stress response of the green microalgae Dunaliella salina (Teod.) after the addition of copper oxide nanoparticles (0, 250, 665, 1330, 2000, 2500, and 3750 µg/L) and ions of copper (0, 15, 150, 200, 400, 580, 770 µg/L) was performed. It was found that the inhibitory effect of copper on the structural and functional characteristics of D. salina was less pronounced when algae were grown on an f/4 nutrient medium, which is explained by the high content of the chelating agent EDTA capable of binding metal ions dissolved in water into chelate complexes, thereby reducing their activity and toxic effect on cells and increasing bioavailability for algae in the medium. A different mechanism of action of ionic and nano copper on the physiology of algae was shown. It was found that the ionic form of copper has a cytotoxic effect on Dunaliella salina cells, while CuO nanoparticles have a mechanical effect on the cell surface. Cell growth retardation, a decrease in fluorescein diacetate (FDA) fluorescence, a decrease in the specific content of chlorophyll per cell, the efficiency of the photosynthetic apparatus, and an induction of ROS synthesis were observed when algae were cultivated on f/32 medium at a concentration of Cu 2+ in the medium above 400 μg/L. The negative effect of CuO nanoparticles (NPs) was found at a pollutant content above 700 µg/L. It had a greater effect on morphological changes in cells: a twofold enlargement of cells occurred, the number of spherical forms increased (up to 71%), and significant deformation and perforation of the plasmalemma and the predominance of deformed cells of irregular shape and cells agglomerated with nanoparticles were found. It has been shown that the maximum concentrations of toxicants studied do not lead to complete elimination of the population, which is probably explained by the presence of cells resistant to copper (approximately 10–15% according to FDA staining) and capable of ensuring the survival and subsequent restoration of the Dunaliella salina population at a high level of anthropogenic pollution of the environment.