Noam Glick was wounded in the chest in Saturday's attack.
She was shot while playing outside her home in Psagot, which is just a few hundred metres from al-Bira.
The suspects were detained in a raid by Israeli troops.
On Sunday Israeli Prime Minister Benjamin Netanyahu condemned the "hateful attack" on the girl and said he held Palestinian leaders responsible even though it took place in an area under full Israeli military control.
"As long as the incitement continues in the Palestinian official media, the Palestinian Authority cannot absolve itself of responsibility for events of this sort," he told a cabinet meeting.
Palestinian Authority President Mahmoud Abbas told Israeli MPs visiting Ramallah on Monday that he opposed "on principle aggression against anyone, and the spilling of blood."
He said the Israeli arrest operation in the Palestinian area was unjustified as it should have been left to Palestinian security forces.
The incident comes as Israeli and Palestinian officials are in the midst of several rounds of peace talks which resumed in August after a three-year hiatus.