Rhodosporidium toruloides is a carotenogenic, oleogenic yeast that is able to grow in diverse environments. In this study, the proteomic and metabolic responses to copper stress in the two haplotypes IFO0559 and IFO0880 were assessed. 0.5 mM Cu(I) extended the lag phase of both strains significantly, while only a small effect was observed for Cu(II) treatment. Other carotenogenic yeasts such as Rhodotorula mucilaginosa are known to accumulate high amounts of carotenoids as a response to oxidative stress, posed by excess copper ion activity. However, no significant increase in carotenoid accumulation for both haplotypes of R. toruloides after 144 h of 0.5 mM Cu(I) or Cu(II) stress was observed. Yet, an increase in lipid production was detected, when exposed to Cu(II), additionally, proteins related to fatty acid biosynthesis were detected in increased amounts under stress conditions. Proteomic analysis revealed that besides the activation of the enzymatic oxidative stress response, excess copper affected iron–sulfur and zinc-containing proteins and caused proteomic adaptation indicative of copper ion accumulation in the vacuole, mitochondria, and Golgi apparatus.