COSINUS is a dark matter (DM) direct search experiment that uses sodium iodide (NaI) crystals as cryogenic calorimeters. Thanks to the low nuclear recoil energy threshold and event-by-event discrimination capability, COSINUS will address the long-standing DM claim made by the DAMA/LIBRA collaboration. The experiment is currently under construction at the Laboratori Nazionali del Gran Sasso, Italy, and employs a large cylindrical water tank as a passive shield to meet the required background rate. However, muon-induced neutrons can mimic a DM signal therefore requiring an active veto system, which is achieved by instrumenting the water tank with an array of photomultiplier tubes (PMTs). This study optimizes the number, arrangement, and trigger conditions of the PMTs as well as the size of an optically invisible region. The objective was to maximize the muon veto efficiency while minimizing the accidental trigger rate due to the ambient and instrumental background. The final configuration predicts a veto efficiency of 99.63 ± 0.16% and 44.4 ± 5.6% in the tagging of muon events and showers of secondary particles, respectively. The active veto will reduce the cosmogenic neutron background rate to 0.11 ± 0.02 cts · kg - 1 · year - 1 , corresponding to less than one background event in the region of interest for the whole COSINUS-1 π exposure of 1000 kg · days.