The incident took place at about 1am local time on Monday (22:00 GMT on Sunday) after Israeli forces blockaded the camp’s entrances with bulldozers, preventing ambulances and journalists from getting inside, residents told Al Jazeera.
The raid was one of the largest operations in years, they said.
The Palestinian health ministry identified the three men killed as Muhammad Abu Zaytoun, 32, Fathi Abu Rizk, 30, and Abdullah Abu Hamdan, 24.
There was no immediate confirmation of the fatalities by the Israeli military.
Israel has conducted a series of incursions in the occupied West Bank since the start of the year, and earlier this month raided Balata where it killed two Palestinians.
On that occasion, the Fatah movement of Palestinian President Mahmud Abbas announced that the two men killed were members of its armed wing, the Al-Aqsa Martyrs Brigades.