Abstract We demonstrate the application of event-driven Timepix3-based detectors in combination with a double-sided velocity-map-imaging spectrometer to record the full 3D momentum of charged particles at the free-electron-laser facility FLASH. We measured the extreme ultraviolet induced fragmentation of N₂ using 250 kHz FLASH bursts with sub-pixel spatial resolution and up to 1.7 ns temporal resolution for photoelectrons. To further demonstrate the capabilities of this camera at even higher repetition rates we measured single-shot images of He(1s) photoelectrons for bursts with a repetition rate of 1 MHz. Overall, with the Timepix3 camera we overcome limitations of standard-camera technology for advanced-imaging experiments with requirements on high event-rates and high spatio-temporal resolution.