In this work, we removed copper (II) from an aqueous solution by using zeolite modified with a silicon-organic monomer (3-aminopropyltriethoxysilane; APTES) depending on the pH, time, temperature, and initial concentration of Cu(II) ions. To confirm the modification process and assess the interaction between the modified zeolite and Cu(II), we performed instrumental analyses (XRD, SEM/EDX, TGA/DTA, BET, FT-IR, and XPS). We determined the maximum adsorption capacities of the modified zeolite for Cu(II) to be 4.50, 6.244, 6.96, and 20.66 mg/g at T = 25 °C (pH = 5, t = 8 h) when the initial concentrations of Cu(II) were 50, 100, 200, and 400 mg/L, respectively. According to the adsorption thermodynamics and kinetics, the second-order reaction controls the adsorption process. Based on the two isotherm models (Langmuir and Freundlich) with constant values (KL = 0.144, n = 2.764) and the correlation coefficients (R2 = 0.8946, R2 = 0.9216), we concluded that the Cu(II) adsorption onto the modified zeolite could be followed by the Freundlich isotherm model rather than the Langmuir isotherm model. The modified zeolite could be an effective material for the removal of Cu(II) from aqueous solutions.