Cisplatin and oxaliplatin are treatment options for a variety of cancer types. While highly efficient in killing cancer cells, both chemotherapeutics cause severe side effects, e.g., peripheral neuropathies. Using a cell viability assay, a mitochondrial stress assay, and live-cell imaging, the effects of cis- or oxaliplatin on the mitochondrial function, reactive oxygen species (ROS) production, and mitochondrial and cytosolic calcium concentration of transient receptor potential ankyrin 1 (TRPA1)- or vanilloid 1 (TRPV1)-positive dorsal root ganglion (DRG) neurons of adult Wistar rats were determined. Mitochondrial functions were impaired after exposure to cis- or oxaliplatin by mitochondrial respiratory chain complex I-III inhibition. The basal respiration, spare respiratory capacity, and the adenosine triphosphate (ATP)-linked respiration were decreased after exposure to 10 µM cis- or oxaliplatin. The ROS production showed an immediate increase, and after reaching the peak, ROS production dropped. Calcium imaging showed an increase in the cytosolic calcium concentration during exposure to 10 µM cis- or oxaliplatin in TRPA1- or TRPV1-positive DRG neurons while the mitochondrial calcium concentration continuously decreased. Our data demonstrate a significant effect of cis- and oxaliplatin on mitochondrial function as an early event of platinum-based drug exposure, suggesting mitochondria as a potential target for preventing chemotherapy-induced neuropathy.