Narrow (~1–2 s) infrasound pulses that followed, with ~11 to ~50 s delays, rapid changes of electrostatic field were observed by a microbarometer array in the Czech Republic during thunderstorm activity. A positive pressure fluctuation (compression phase) always preceded decompression; the compression was usually higher than the decompression. The angles of arrival (azimuth and elevation) were analyzed for selected distinct events. Comparisons of distances and azimuths of infrasound sources from the center of microbarometer array with lightning locations determined by the European Cooperation for Lighting Detection lightning detection network show that most of the selected events can be very likely associated with intracloud (IC) discharges. The preceding rapid changes of electrostatic field, their potential association with IC discharges, and high-elevation angles of arrival for near infrasound sources indicate that an electrostatic mechanism is probably responsible for their generation. It is discussed that distinguishing the relative role of thermal and electrostatic mechanism is difficult and that none of the published models of electrostatic production of infrasound thunder can explain the presented observations precisely. A modification of the current models, based on consideration of at least two charged layers, is suggested. Further theoretical and experimental investigations are however needed to get a better description of the generation mechanism.