Several researchers have studied the source parameters of the 2005 Fukuoka (northwestern Kyushu Island, Japan) earthquake (MW 6.6) using teleseismic, strong motion and geodetic data. However, in all previous studies, errors of the estimated fault solutions have been neglected, making it impossible to assess the reliability of the reported solutions. We use Bayesian inference to estimate the location, geometry and slip parameters of the fault and their uncertainties using Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) data. The offshore location of the earthquake makes the fault parameter estimation challenging, with geodetic data coverage mostly to the southeast of the earthquake. To constrain the fault parameters, we use a priori constraints on the magnitude of the earthquake and the location of the fault with respect to the aftershock distribution and find that the estimated fault slip ranges from 1.5 m to 2.5 m with decreasing probability. The marginal distributions of the source parameters show that the location of the western end of the fault is poorly constrained by the data whereas that of the eastern end, located closer to the shore, is better resolved. We propagate the uncertainties of the fault model and calculate the variability of Coulomb failure stress changes for the nearby Kego fault, located directly below Fukuoka city, showing that the mainshock increased stress on the fault and brought it closer to failure.