Oxycodone is a strong opioid frequently used as an analgesic. Although proven efficacious in the management of moderate to severe acute pain and cancer pain, use of oxycodone imposes a risk of adverse effects such as addiction, overdose, and death. Fast and accurate determination of oxycodone blood concentration would enable personalized dosing and monitoring of the analgesic as well as quick diagnostics of possible overdose in emergency care. However, in addition to the parent drug, several metabolites are always present in the blood after a dose of oxycodone, and to date, there is no electrochemical data available on any of these metabolites. In this paper, a single-walled carbon nanotube (SWCNT) electrode and a Nafion-coated SWCNT electrode were used, for the first time, to study the electrochemical behavior of oxycodone and its two main metabolites, noroxycodone and oxymorphone. Both electrode types could selectively detect oxycodone in the presence of noroxycodone and oxymorphone. However, we have previously shown that addition of a Nafion coating on top of the SWCNT electrode is essential for direct measurements in complex biological matrices. Thus, the Nafion/SWCNT electrode was further characterized and used for measuring clinically relevant concentrations of oxycodone in buffer solution. The limit of detection for oxycodone with the Nafion/SWCNT sensor was 85 nM, and the linear range was 0.5–10 μM in buffer solution. This study shows that the fabricated Nafion/SWCNT sensor has potential to be applied in clinical concentration measurements.