Police spokeswoman Luba Samri says an initial investigation suggests the girl fought with her family before leaving her home with a knife ahead of Saturday's altercation.
The last four months have seen near-daily Palestinian stabbing attacks that have killed 25 Israelis and an American student.
At least 147 Palestinians have been killed by Israeli fire, 102 of them identified by Israel as attackers. The rest have been killed in clashes with Israeli troops.
Israel says the violence is the result of a Palestinian campaign of incitement. The Palestinians say it is rooted in frustration over Israel's nearly 50-year occupation.