Wind energy (WE), which is one of the renewable energy (RE) sources for generating electricity, has been making a significant contribution to obtaining clean and green energy in recent years. Fitting an appropriate statistical distribution to the wind speed (WS) data is crucial in analyzing and estimating WE potential. Once the best suitable statistical distribution for WS data is determined, WE potential and potential yield could be estimated with high accuracy. The main objective of this paper is to propose a novel approach for calculating wind energy potential. For this purpose, the Efficient Global Optimization (EGO) technique was proposed for fitting a statistical distribution to WS data and the performance of the technique was compared with genetic algorithm (GA), simulated annealing (SA), and differential evolution (DE). Performance metrics showed that EGO is providing better estimations compared with GA, SA, and DE. Based on Weibull parameters obtained by using EGO, potential WE and potential annual revenue were estimated for Gdańsk, which is the capital of Pomerania Voivodeship in Poland, in the case of having city-type wind turbines in the city center. Estimations for Gdańsk showed that city-type wind turbines might be helpful for producing electricity from WE in the city without being limited by constraints such as having a long distance between wind turbines and buildings. If such wind turbines were erected on the roofs of residential buildings, malls, or office buildings, there is a possibility that part of the electric energy needed for such buildings could be generated using WE. However, this topic should be further investigated from technical and financial perspectives.