Astrometric gravitational microlensing can be used to determine the mass of a single star (the lens) with an accuracy of a few percent. To do so, precise measurements of the angular separations between lens and background star with an accuracy below 1 milli-arcsecond at different epochs are needed. Therefore only the most accurate instruments can be used. However, since the timescale is on the order of months to years, the astrometric deflection might be detected by Gaia, even though each star is only observed on a low cadence. We want to show how accurately Gaia can determine the mass of the lensing star. Using conservative assumptions based on the results of the second Gaia data release (GaiaDR2), we simulated the individual Gaia measurements for 501 predicted astrometric microlensing events during the Gaia era (2014.5 - 2026.5). For this purpose we used the astrometric parameters of Gaia DR2, as well as an approximative mass based on the absolute G magnitude. By fitting the motion of the lens and source simultaneously, we then reconstructed the 11 parameters of the lensing event. For lenses passing by multiple background sources, we also fitted the motion of all background sources and the lens simultaneously. Using a Monte-Carlo simulation we determined the achievable precision of the mass determination. We find that Gaia can detect the astrometric deflection for 114 events. Furthermore, for 13 events Gaia can determine the mass of the lens with a precision better than 15% and for 13 + 21 = 34 events with a precision of 30% or better.