Soldiers found an improvised weapon outside the settlement that may have been used by the suspected terrorist as well as a breach in the security fence around the settlement.
Israeli Prime Minister Binyamin Netanyahu Sunday condemned the attack and cited a recent increase in West Bank terrorist activity.
"I must say as long as incitement in the official Palestinian media continues, the Palestinian Authority cannot rid itself of the responsibility for such incidents," Israel Radio quoted Netanyahu as saying.
Psagot is located near Ramallah by the Palestinian town el-Bireh.
The young girl, Noam Glick, was playing in the yard of her Psagot home Saturday night when she was attacked. Noam was taken to a hospital in Jerusalem with injuries to her chest and neck. Israeli military officials said it was unclear whether her injuries were the result of a shooting or stabbing.
Noam's father, Yisrael Glick, told Army Radio he heard gunshots and his daughter told him an Arab was outside. He said he pulled her into the house and by the time he got his weapon the suspect had fled.
Israeli security officials noted Hamas in Gaza is trying to "heat up" the area and has intensified its efforts to boost its presence in the West Bank with the aim of abducting Israeli soldiers or civilians, the radio report said.