Cyanobacteria and their toxins present potential hazards to consumers of water from lakes, reservoirs and rivers; thus, their removal via water treatment is essential. Previously, we demonstrated that nanocomposites of octadecyltrimethyl ammonium (ODTMA) complexed with clay could efficiently remove cyanobacteria and their toxins from laboratory cultures and lake water. In this study, we determined the capacity of ODTMA nanocomposites to remove cyanotoxins, namely microcystins (MCs), from water to below 1 µg/L via filtration. This capacity was 1500 mg MC-LR per Kg of nanocomposite. Similar capacities were estimated for the removal of other MC congeners (MC-WR, MC-3aspWR and MC-YR), whereas substantially lower capacities were recorded for more positively charged MC congeners, such as MC-RR and MC-3aspRR. Filtration results were simulated with a filtration model, which considers convection and adsorption/desorption of one to several toxins. Model calculations for the removal of MC-LR, under a variety of situations, fitted well with all the experimentally measured values and also estimated the co-removal of several MC congeners. In agreement with model predictions, results demonstrated that in the presence of MC-WR, the emerging concentrations of MC-RR congeners eventually exceed their solution values. In conclusion, granulated nanocomposites of ODTMA–bentonite can be applied for the removal of microcystins from drinking water.