He will be kept under house detention for nine days, lawyer Ziad Haidimi said after a court session.
If the investigation ends without charges, he can travel back to the United States, Haidimi said. His mother, Suha Abu Khdeir, said the family "definitely" will sue Israeli authorities.
"I'm not really happy" with the court's decision, she said.
The teen's aunt said he was scared, lost and confused.
"You just wish you could have pulled him out of that situation as soon as you could," Sanah Abukhdeir told CNN.
"Tariq doesn't understand anything that's going on as far as war. He hasn't been in any type of war zone before, so all of this is really scary for him," she said.
An official from the U.S. Consulate General was at Khdeir's hearing Sunday.
"We will continue to monitor the situation closely," U.S. State Department spokeswoman Jen Psaki said in a statement. "We are calling for a speedy, transparent and credible investigation and full accountability for the apparent excessive use of force."
Israel's ambassador to the United States told "Fox News Sunday" there will be justice and that excessive use of force is unacceptable.
"I will tell you, from what I understand about the facts of the case, this is not just an innocent bystander who was pulled off of a schoolyard," Ron Dermer said Sunday. "He was with six other people. They were masked. They threw petrol bombs and Molotov cocktails at our police. Three of them had knives, from what I understand.
"That does not excuse any excessive use of force and our Justice Ministry is opening an investigation."
According to his family, Tariq was among the Palestinians protesting in the Shuafat neighborhood over his cousin's killing. But he wasn't involved in the clashes, they say. His relatives say he is the young man who appears in two separate videos being held down and beaten by men wearing the uniform of Israeli security forces.
His father, Salah Eddeine Abu Khdeir, said Saturday that his son didn't throw rocks at police.
Netanyahu on Sunday said the other side must help calm tensions.
"I call on the leaders of the Arab public to show responsibility and come out against the disturbances in order to restore quiet," he said.