The man, Salim al-Sir, was a 32-year-old member of the military wing of the political group Hamas. He was shot in the head.
Earlier a Palestinian policeman, Ibrahim al-Bayuk, 27, and a fighter from the Abu al-Rish Brigades were killed and six other people wounded in the camp during exchanges of fire with invading Israeli forces.
Witnesses said some Palestinian families fled their homes as about 50 Israeli armoured vehicles, including bulldozers, backed by helicopter gunships as well as surveillance aircraft, rumbled into Khan Yunus at the start of the invasion on Tuesday night.
Aljazeera's correspondent in Gaza reported that the fighter was Muhammad al-Jaraitli, 23, a member of the Abu al-Rish Brigades, linked to the Fatah movement.
An Israeli military spokesman said soldiers had killed or injured a Palestinian who was firing at them during the invasion, which is set to last about two days.
The Israeli army said the move was to halt attacks on Jewish settlements. Settlements are illegal under international law.
Residents said bulldozers destroyed the rest of a clinic damaged in an earlier raid and also raided a school.
Separately, Israeli troops shot dead a Palestinian who tried to scale the border fence out of the northern Gaza Strip.
Medics were prevented from reaching the man, who bled for several hours before dying of his wounds.
In the West Bank, an Israeli security guard - working for a construction firm charged with building the barrier wall - was killed and another wounded near Hebron on Wednesday afternoon.
An injured Palestinian is rushed
to hospital in Khan Yunus
The Israeli army said Palestinian gunfire near the border between Israel and the Hebron region of the southern West Bank caused the casualties.
Israeli troop movements were also reported at the northern entrance to the Gaza Strip, where Palestinians have been firing rockets at Israeli towns just outside the territory.
According to Aljazeera's correspondent, Israeli forces have also launched a raid on Asira, a town north of Nablus city.
Two Palestinians were injured in the raid and a curfew was imposed on the town.
Seven other Palestinians were detained in different parts of the West Bank overnight.