Despite the increasing demand for offshore energy, structural components of offshore wind turbines (OWT), such as the tower and foundation, are considered the most critical parts of the turbine. In fact, uncertainties regarding load conditions, soil and structural properties highly undermine the OWT structural reliability. In this scenario, in order to obtain more accurate results, rigorous probabilistic analyses are necessary. In this study, a probabilistic analysis of the dynamic response of a monopile OWT is conducted by using a systematic uncertainty quantification (UQ) framework to deal with the uncertainty assessment of the model input parameters. The proposed dynamic model computes the dynamic response of the turbine due to wind and waves loads on the monopile structure utilizing a simple cantilever beam analytical model. The distributions of the model input parameters are determined using (1) nonparametric statistics for a large dataset, and (2) the maximum entropy principle for a small dataset. Monte Carlo simulations are performed to propagate the uncertainties of the model inputs and to determine the system reliability expressed in terms of their probability of failure for the serviceability limit state design criterion. Finally, to demonstrate the shortcomings of traditional approaches that assume standard distributions to model uncertainties, a UQ approach modeling the uncertainties of the parameters using normal distributions is contrasted with our framework. From the results, significant differences between the distribution shape and values of the probability of failure can be observed; thus, it demonstrates the importance of developing probabilistic frameworks with systematic UQ to have more realistic approximations of the reliability of the OWT structure.