A statement purporting to come from Hamas said the militant Palestinian group had carried out the operation.
The soldiers were lured to a jeep which appeared to be stuck in the sand, near the Jewish settlement of Dugit in the northern part of the strip.
As the soldiers approached, a man inside the vehicle blew it up. The blast was so powerful that only the jeeps axle was left.
A statement purporting to come from Hamas said the militant Palestinian group had carried out the operation.
Palestinian officials said three Palestinians were seriously wounded when an Israeli tank opened fire following the bomb.
Friday's attack brought the total number killed since a US-brokered ceasefire was announced last week to 12 - including three Jewish settlers, three soldiers and six Palestinians.
Protests
Earlier on Friday, Jewish settlers had mounted a series of protests in the West Bank to vent their anger at their government's continued support for the current ceasefire with the Palestinians, despite the killing of settlers by gunmen.
Palestinian traffic was backed up at Halhoul junction near Hebron, as settlers threw stones at cars, causing damage but no injuries, and two Palestinian journalists were beaten in the city itself.
Witnesses said armed settlers also ran amok near Ramallah, where they burned crops, and near Nablus, where they set fire to olive trees and attacked the driver of a fire truck sent to tackle the blaze.
Battle against time
Security officials from both sides have meanwhile held another meeting to discuss fundamental differences over their truce.
The ceasefire proposals - laid down by the head of the American CIA, George Tenet, and grudgingly accepted by both sides - say a six-week ceasefire should lead to resumed peace negotiations.
Top officials from the United States and the European Union are also engaged in a race against the clock to prevent the ceasefire from collapsing.
US envoy William Burns met Israeli Foreign Minister Shimon Peres on Friday.
EU foreign policy chief Javier Solana held separate meetings which he described as "good and constructive" with Mr Peres, Prime Minister Ariel Sharon and the Palestinian leader Yasser Arafat on Friday.
The Palestinians say Israel should lift travel restrictions and roadblocks and pull back troops and heavy equipment within two weeks; Israel says the redeployment would take four weeks but can only start when all Palestinian violence stops.
Settlers' leaders are threatening to rise up against Mr Sharon unless he abandons the ceasefire and imposes a military solution to nearly nine months of bloodshed.
The settlers have been told by the army to travel in convoys or armoured vehicles as they pass through the West Bank.
But one settler said that offers little protection, as the attackers "aren't afraid because they know there is no response".
About 200,000 Jews live on land captured by Israeli in 1967 in settlements deemed illegal under international law.