Witnesses and military sources said the explosion on Wednesday targeted a military position guarding the entrance to Morag - a settlement close to Gaza's southern border with Egypt.
Confirming the blast toll, an Israeli military source said explosives may have been placed in a tunnel.
But the Islamic Jihad resistance movement, which claimed responsibility for the attack, said two of its members had planted a bomb under an Israeli military vehicle.
Islamic Jihad added that it knew at least one of its fighters had also died in the attack and had not yet contacted the other.
Palestinian witnesses said the blast hit a military vehicle, wounding several soldiers who were evacuated by helicopter.
Five soldiers were killed on 12 December when resistance fighters blew up an explosives-packed tunnel and attacked an Israeli border crossing in the same area.