Ammonium ion is a chemical species that is found in abundance in natural waters, whether underground or surface, but also in wastewater resulting from agricultural and industrial activities. Even if the removal of the ammonium ion from water has been studied for a very long time, it has been found that its removal is far from being solved. In this study, we evaluated the performance of the ammonium ion adsorption process on two adsorbents, zeolite clinoptilolite, ZR, a sustainable material (manufacturer: Zeolite Development SRL, Rupea, Brasov, Romania), and the other granular activated carbon type, Norit GAC 830 W. Zeolite ZR is found in very large deposits in Romania; it is a natural, cheap material with costs between 50 and 100 EUR/ton, compared to other adsorbents that cost over 500 EUR/ton and which can be regenerated and reused in the technological process of water treatment and purification, but also after exhaustion, as an amendment for the soil. In the first step, this paper presents the mineralogic (XRD) and structural (SEM and EDX) characterization of the ZR and the determination of the pH zero-point charge, pHZPC, for all the adsorbents. Studies were carried out in equilibrium and kinetic conditions. The efficiency of the adsorbent was investigated in different experimental conditions by varying the initial concentration, particle size, temperature, pH, ionic strength, and contact time. The mathematical models and parameters specific to the adsorption isotherms that best describe the experimental results were identified. Langmuir, Freundlich, Temkin, and Dubinin–Radushkevich mathematical models were used for comparison. The Langmuir isotherm proved to be the most appropriate to describe the adsorption of ammonium ions on all types of adsorbents used. The adsorption capacity of ammonium ions from synthetic solutions at 20 °C, pH = 6.09, for the range of initial concentrations 0–50 mg/L for Rupea zeolite is in the range of 10.46 mg/g−12.34 mg/g, and for granular activated carbon GAC W830, it is 16.64 mg/g. It was found that the adsorption capacity of the ammonium ion on both activated carbon and zeolite increases with increasing temperature and pH. Also, it was observed that as the ionic strength increases, the adsorption capacity decreases for all four adsorbents. Kinetic models were also identified that best describe the experimental processes. In this sense, pseudo-first order, pseudo-second order, intra-particle diffusion and the Elovich model were used. The results of the investigation showed that second-order kinetics governs the adsorption process on ZR, and pseudo-first order governs activated carbon.