The army said four people "attempted to infiltrate" by breaking through the security fence.
"Troops arrived at the scene and fired shots towards the terrorists, as a result of which three were killed," an army statement said.
It added that a bag was found with cutters, an axe and other materials.
Gaza's health ministry identified two of the dead as Bahaa Rahman Qudeih, 23, and Mohammed Abu Rayda, 20. A name had not yet been provided for the third person.
The latest deaths raised to 52 the toll of Palestinians killed by Israeli forces since protests and clashes began along the Gaza border on March 30.
Hundreds more have been wounded by gunfire.
Demonstrators are demanding Palestinian refugees be allowed to return to the homes they fled or were expelled from during the 1948 war surrounding Israel's creation.
Israel argues allowing the so-called right of return would effectively spell the end of the country as a Jewish state.
No Israelis have been hurt in the weeks of protests and the military has faced international criticism for its use of live ammunition.
It says it only opens fire when necessary to stop infiltrations, attacks and attempts to damage the fence.
It accuses Hamas, the Islamist movement that runs the Gaza Strip and with whom it has fought three wars since 2008, of seeking to use the protests as cover to carry out violence.
Overnight Israel struck a facility belonging to Hamas in reaction to kite-borne fire bombings, which have reportedly caused significant damage to Israeli fields.
