Biomass of the invasive seaweed Sargassum muticum harvested from the Atlantic coast of Morocco was investigated as a natural biosorbent for the removal of methylene blue (MB) dye from aqueous solutions. FTIR spectroscopy was used to examine the variability of functional groups participating in the interaction between MB and biosorbent. The zero point charge (pHZPC) of the biomass was about 5.45. The factors affecting the efficiency of the biosorption process such as the biosorbent dose, the initial solution pH, the initial dye concentration and the contact time were investigated. The theoretical monolayer saturation capacity was estimated to be 191.38 mg/g. The biosorption process was generally not dependent on pH for values ranging from 2 to 10. The biosorption occurs very fast in the first 5 min and reaches the equilibrium within 60–90 min. The pseudo-second-order model was found to explain the adsorption kinetics most effectively. Four conventional isotherm models were applied to describe the biosorption equilibrium data and classified according to their correlation coefficients in the following order: Temkin model (R2 = 0.989) > Dubinin–Radushkevich (R2 = 0.982) > Langmuir (R2 = 0.938) > Freundlich (R2 = 0.934). The Temkin constants (KT = 0.825 L/g, bT = 43.165 J/mol) and the Dubinin–Radushkevich mean free energy (ED= 0.731 kJ/mol) indicated that the adsorption of MB onto the biomass of the invasive seaweed could be a physisorption process. The values of the thermodynamic parameters showed that adsorption is a spontaneous and exothermic process. This study suggests that biomass of the invasive seaweed Sargassum muticum has a good potential capacity to remove MB dye and it could offer promising opportunity, as a low-cost biosorbent for the treatment of cationic dye industrial wastewaters.