The commanding officer at the scene fired a shot into the air, and a soldier opened fire on the approaching figure.
Al-Kadr was hit in the hand by a bullet, leaving her seriously wounded. She died on the way to hospital in Tel Aviv.
Palestinian sources said the second girl was seriously wounded, but the Israeli army said she suffered only from shock.
The army called the incident a very serious matter, adding that the soldier who fired the shots had not been authorised to do so.
Preliminary results from an investigation have revealed that the soldier opened fire of his own accord.
The Israeli army central command ordered the officer and the soldier who fired the shots to be suspended from all activities, and has launched an investigation.
Rights of the child
The UN Convention on the Rights of the Child guarantees the fundamental rights of all children. Israel signed and ratified this agreement in October 1991.
"It's been one of the deadliest years that we have seen"
Dan Rohrmann, Unicef
However, according to the Palestine Monitor, between September 2000 and July 2006, 783 Palestinian children under the age of 18 have been killed by the Israeli army and Israeli settlers.
The Palestine Monitor is a civil society group that sources information from Palestinian, US and European NGOs.
This figure is almost 22% of the total number of Palestinians killed in that time.
According to the Palestinian health ministry, 2,660 Palestinian children have been permanently disabled due to Israeli attacks in the same period.
Misuse of weapons
Unicef has said that 123 Palestinian children have been killed in 2006, which is more than double the 2005 figure. In Gaza alone, 103 children have been killed.
Dan Rohrmann, Unicef's special representative in the occupied Palestinian territory, said: "This has been a tragic year for Palestinians living in Gaza and the West Bank.
"It's been one of the deadliest years that we have seen."