The presence of dyes in waterbodies poses severe problems in human and aquatic creatures, and the development of treatment methods for the removal of these pollutants is of utmost importance. This research study investigates the elimination of methylene blue (MB) from an aqueous solution using zero-valent iron nanoparticles synthesized from sweet lime pulp waste (nZVISLP). The purity, chemical composition, and crystalline size of nZVISLP were investigated using microscopic and spectroscopic studies. A maximum MB removal efficiency of 98.9% was obtained at the following optimal conditions: C0: 10 mg/L, dosage: 1.2 g/L, and temperature: 25 °C. To understand the adsorptive removal characteristics of nZVISLP, the investigational adsorption data were tested with conventional kinetic and isotherm models. Furthermore, a differential evolution optimization (DEO) technique was used to estimate the optimal intrinsic parameters in the isotherm and kinetic models. For the various evaluated isotherms, the correlation coefficient (R2) values for the Freundlich and Sips isotherm models were ~0.98, thus confirming the aptness of these isotherms to represent MB adsorption onto nZVISLP. The robustness of non-linear models was verified by statistical metrics, thus validating the performance of the optimization technique. The results derived from this study affirm the potential of an ecofriendly biogenic nanomaterial, nZVISLP, for MB adsorptive removal.