Marine plastic pollution is one of the most concerning worldwide environmental issues, and research is day by day demonstrating its adverse effects on marine ecosystems. Nevertheless, little is still known about the toxic potential on marine fauna of chemical additives released by plastic debris. Here we investigated the cyto- and genotoxicity of the most used plasticizer in plastic production, di(2-ethylhexyl)phthalate (DEHP), on a skin cell line (TT) derived from the bottlenose dolphin (Tursiops truncatus), a species particularly exposed to the accumulation of this lipophilic pollutant, being a coastal top predator rich in fatty subcutaneous tissues. Dolphin cell cultures were exposed to increasing DEHP doses (0.01–5 mM) to evaluate effects on cell viability, cell death, and induction of DNA damage. On the hypothesis that bottlenose dolphin cells show greater resistance to DEHP toxicity than terrestrial mammals, as already shown for other pollutants, the same parameters were analyzed on exposed Chinese hamster ovary (CHO) cell lines. Both MTT and Trypan Blue assays showed no significant decrease in dolphin’s cell viability after 24-h DEHP exposure. No induction of primary DNA damage was detected by the comet assay, whereas the cytokinesis-block micronucleus assay revealed significant micronuclei induction and inhibition of cell proliferation starting from the lowest DEHP doses. DEHP had similar but sharper and significant effects on cell viability in CHO cells, also causing a much greater induction of necrosis than that recorded on dolphin cells. For both cell lines, the lack of induction of primary DNA damage (i.e., strand breaks) together with the increase of micronuclei yield after DEHP treatment suggests an aneugenic effect of the phthalate, that is, the loss of entire chromosomes during cell division. Overall, the potential chromosome loss detected could constitute a threat for species of marine mammals constantly exposed to plastic marine litter.