Trace analysis of heavy metals in complex, environmentally relevant matrices remains a significant challenge for electrochemical sensors employing stripping voltammetry-based detection schemes. We present an alternative method capable of selectively preconcentrating Cu²⁺ ions at the electrode surface using chelating polymer-wrapped multiwalled carbon nanotubes (MWCNTs). An electrochemical sensor consisting of poly-4-vinyl pyridine (P4VP)-wrapped MWCNTs anchored to a poly(ethylene terephthalate) (PET)-modified gold electrode (r = 1.5 mm) was designed, produced, and evaluated. The P4VP is shown to form a strong association with Cu²⁺ ions, permitting preconcentration adjacent to the electrode surface for interrogation via cyclic voltammetry. The sensor exhibited a detection limit of 0.5 ppm with a linear range of 1.1–13.8 ppm (16.6–216 μM) and a relative standard deviation (RSD) of 4.9% at the Environmental Protection Agency (EPA) limit of 1.3 ppm. Evaluation in tap water, lake water, ocean water, and deionized water rendered similar results, highlighting the generalizability of the presented preconcentration strategy. The advantages of electrochemical analysis paired with polymeric chelation represent an effective platform for the design and deployment of heavy metal sensors for continuous monitoring of natural waters.