With wind power providing an increasing amount of electricity worldwide, the quantification of its spatio-temporal variations and the related uncertainty is crucial for energy planners and policy-makers. Here, we propose a methodological framework which (1) uses machine learning to reconstruct a spatio-temporal field of wind speed on a regular grid from spatially irregularly distributed measurements and (2) transforms the wind speed to wind power estimates. Estimates of both model and prediction uncertainties, and of their propagation after transforming wind speed to power, are provided without any assumptions on data distributions. The methodology is applied to study hourly wind power potential on a grid of 250 x 250 m(2) for turbines of 100 m hub height in Switzerland, generating the first dataset of its type for the country. We show that the average annual power generation per turbine is 4.4 GWh. Results suggest that around 12,000 wind turbines could be installed on all 19,617 km(2) of available area in Switzerland resulting in a maximum technical wind potential of 53 TWh. To achieve the Swiss expansion goals of wind power for 2050, around 1000 turbines would be sufficient, corresponding to only 8% of the maximum estimated potential.