The alleged attack has taken place at 8:40 pm on Monday at the Bab Huta entrance to the Temple Mount shortly before Muslim night-time prayers, according to Israeli media.
The police say the Palestinian boy has moderately wounded a Border Police officer before being shot dead by other officers at the scene.
A woman who was standing nearby has also been apparently hit by a ricochet and lightly injured. She was taken to a hospital for treatment, police said.
Police has closed off the area, including the Temple Mount.
Human rights groups have repeatedly criticized the Tel Aviv regime for its shoot-to-kill policy as a large number of the Palestinians killed at the scene of the alleged attacks did not pose serious threats to Israelis.
Israeli troops have on numerous occasions been caught on camera brutally killing Palestinians, with the videos going viral online and sparking international condemnation.