Heavy metal ions (HMIs) are major water pollutants, and their toxicity for humans is a great concern for scientists and environmentalists. They are harmful to health even at trace levels; therefore, identifying and removing heavy metals from water is critical. Herein, we report highly selective and sensitive multi-analyte detection of HMIs in water using an electrochemical sensor probe based on Ag nanoparticles and single-walled carbon nanotubes incorporating copper benzene tri-carboxylate metal–organic frameworks (Ag/SWNTs@CuBTC-MOFs). The materials were characterized using FTIR, XPS, XRD, and FE-SEM with EDX mapping, TEM, TG-DTA, BET surface area, CV, and EIS. The Ag/SWNTs@CuBTC-MOF electrochemical sensor was tested by differential pulse voltammetry over a pH range of 3–10 for various HMIs. It shows high pH-dependent sensitivity towards Hg2+ (pH-5.0), Ni2+ (pH-7.0), and Fe3+ (pH-10.0) ions and a limit of detection of 1.39 nM, 2.6 nM, and 3.03 nM, respectively. The fabricated sensor probe exhibits high selectivity, good linearity, and a limit of detection below the maximum contamination limit, as the US Environmental Protection Agency suggested.