Time-domain studies of pre-main-sequence (PMS) stars have long been used to investigate star properties during their early evolutionary phases and to trace the evolution of circumstellar environments. Historically these studies have been confined to the nearest, low-density, star-forming regions. We used the Wide Field Camera 3 on board the Hubble Space Telescope to extend, for the first time, the study of PMS variability to one of the few young massive clusters in the Milky Way, Westerlund 2. Our analysis reveals that at least one-third of the intermediate- and low-mass PMS stars in Westerlund 2 are variable. Based on the characteristics of their light curves, we classified similar to 11% of the variable stars as weak-line T Tauri candidates, similar to 52% as classical T Tauri candidates, similar to 5% as dippers, and similar to 26% as bursters. In addition, we found that 2% of the stars below 6 M (similar to 6% of the variables) are eclipsing binaries, with orbital periods shorter than 80 days. The spatial distribution of the different populations of variable PMS stars suggests that stellar feedback and UV radiation from massive stars play an important role in the evolution of circumstellar and planetary disks.