The synthesis of Co-based two-dimensional (2D) metal azolate framework nanosheets (MAF-5-Co^II NS) is described using a simple hydrothermal method. The product was isostructural to MAF-5 (Zn). The as-prepared MAF-5-Co^II NS exhibited high surface area (1155 m²/g), purity, and crystallinity. The MAF-5-Co^II NS–modified screen-printed electrode (MAF-5-Co^II NS/SPE) was used for nonenzymatic detection of glucose in diluted human blood plasma (BP) samples with phosphate buffer saline (PBS, pH 7.4) and NaOH (0.1 M, pH 13.0) solutions. The MAF-5-Co^II NS nanozyme displayed good redox activity in both neutral and alkaline media with the formation of Co^II/Co^III redox pair, which induced the catalytic oxidation of glucose. Under the optimized detection potential, the sensor presented a chronoamperometric current response for the oxidation of glucose with two wide concentration ranges in PBS-diluted (62.80 to 180 μM and 305 to 8055 μM) and NaOH-diluted (58.90 to 117.6 μM and 180 to 10,055 μM) BP samples, which were within the limit of blood glucose levels of diabetic patients before (4.4–7.2 mM) and after (10 mM) meals (recommended by the American Diabetes Association). The sensor has a limit of detection of ca. 0.25 and 0.05 μM, respectively, and maximum sensitivity of ca. 36.55 and 1361.65 mA/cm²/mM, respectively, in PBS- and NaOH-diluted BP samples. The sensor also displayed excellent stability in the neutral and alkaline media due to the existence of hydrophobic linkers (2-ethyl imidazole) in the MAF-5-Co^II NS, good repeatability and reproducibility, and interference-free signals. Thus, MAF-5-Co^II NS is a promising nanozyme for the development of the disposable type of sensor for glucose detection in human body fluids.