A silica aerogel/MgO composite synthesized from bagasse ash was investigated as a biomass-derived adsorbent for the removal of malachite green from aqueous solutions. The adsorption performance was systematically assessed through operational parameters, adsorption kinetics, equilibrium isotherms, and thermodynamic analyses. Comparative experiments demonstrated the superior adsorption capability of the silica aerogel/MgO composite relative to pristine silica aerogel, with adsorption capacities of 96.93 and 22.12 mg/g, respectively, recorded under the same experimental conditions, highlighting the beneficial interaction between the porous silica framework and MgO active sites. Equilibrium was attained after 80 min of contact time, and under optimum conditions, the composite achieved an adsorption capacity of 123.19 mg/g at 45°C with an initial dye concentration of 55 mg/L, while the highest removal efficiency (90.93%) was obtained at pH 9. Kinetic analysis revealed that the pseudo-second-order model most accurately represented the experimental data, yielding an R² value of 0.9923. Equilibrium studies further indicated that the Freundlich isotherm provided the best fit (R² = 0.9965–0.9973), suggesting adsorption on energetically heterogeneous surfaces with the possibility of multilayer uptake. Thermodynamic evaluation confirmed that the adsorption process occurred spontaneously and was favored at elevated temperatures, as evidenced by negative Gibbs free energy values (ΔG° = −4.68 to −6.29 kJ/mol), positive enthalpy changes (ΔH° = 12.46–15.29 kJ/mol), and positive entropy values (ΔS° = 58.76–67.10 J/mol·K). Overall, the results demonstrate the strong potential of the bagasse ash-derived silica aerogel/MgO composite as an efficient and sustainable adsorbent for the removal of cationic dyes from water.