Al-Aqsa Martyrs Brigades claimed responsibility for the attack on Saturday, reported Aljazeer's correspondent in Palestine.
The Israeli army had no immediate comment.
The death was Israel's first in the Palestinian territories since a string of ambushes in mid-May killed 13 troops in the Gaza Strip, triggering a six-day raid in Rafah in which 42 Palestinians were killed and dozens of homes were destroyed.
Witnesses saw medics treating a soldier lying in a pool of blood, after he was shot in an exchange of fire with resistance fighters during an early morning raid.
Meanwhile, in a separate incident, a Palestinian man's body was found near the Gaza border fence with Israel. "He was shot on suspicion of trying to plant a bomb," an Israeli military source said.
The source said Palestinians had recovered the man's body lying near the border fence with Israel east of the northern Gaza town of Bait Hanun. Two bombs were found nearby.
The soldier was killed after
clashes with Palestinian fighters
Elsewhere in the West Bank, soldiers arrested four suspected Palestinian fighters early on Saturday in villages near the town of Ram Allah.
Also on Saturday, an Israeli man was stabbed in the back by a Palestinian in Jerusalem's Old City, according to the police.
The attack took place on a major street that runs through the Muslim Quarter of the walled Old City. The man arrived under his own power at the Western Wall, where he was treated and then evacuated to the hospital in light to moderate condition, police said.
The Old City, which contains shrines holy to Muslims, Jews and Christians, is an emotional flashpoint in the conflict between Israelis and Palestinians.