Although the installation of offshore wind turbines takes place in calm seas, successful mating of wind turbine components can be challenging due to the relative motions between the two mating parts. This work investigates the effect of a passive tuned mass damper on the mating processes of a nacelle for a 10-megawatt (MW) offshore wind turbine. A nacelle with lifting wires and a monopile with a mass damper are respectively modelled using the multibody formulation in the HAWC2 program. A single mass damper is tuned to target at the first natural period of the monopile and is coupled to the main program using a dynamic link library. Afterwards, numerical simulations were carried out in turbulent wind conditions and irregular wave conditions typical of offshore installation scenarios. Important response variables including the tower-top motions, nacelle motions, and their relative motions are examined in the analysis. By comparing the time series and response statistics, we found that the tower-top motion is more crucial to the installation process than the lifted nacelle motion. For the relative motions and velocities between the nacelle and the tower top, the tuned mass damper can reduce the short-term maximum values by more than 50% for the examined sea states with spectral period between 4 to 12 seconds. This implies that the weather window for marine operations can be expanded if the tuned mass damper is applied.