By Agence France-Presse
The body of Ori Ansbaher, 19, was found on Thursday evening in the south of Jerusalem, and she was buried on Friday in the Israeli settlement of Tekoa.
The suspect comes from the flashpoint city of Hebron in the south of the occupied West Bank, police said.
All other details of the woman's killing remain the subject of an Israeli gag order.
Previous Israeli statements about her murder came only from top diplomats and politicians.
Israel's ambassador to the United Nations, Danny Danon, accused the UN Security Council of staying silent in the face of what he charged was the complicity of the Palestinian Authority (PA) of president Mahmud Abbas in such attacks.
"The PA maintains its policy of paying salaries for terrorists and educating its youth with incitement, and a 19-year-old girl was brutally murdered in Israel," he said.
"The Security Council has the responsibility and moral duty to make a clear condemnation of this barbaric murder and to act firmly against the culture of terror in the Palestinian Authority."
Prime Minister Benjamin Netanyahu vowed in a statement on Friday evening that "the security forces will track down those responsible for this killing and we will treat them with the full force of the law."
Netanyahu's principal challenger in an April 9 general election, former armed forces chief of staff Benny Gantz, said he had full confidence in the ability of the security forces to arrest the killer.
The West Bank was hit by a bout of unrest in December as tensions eased in the Gaza Strip. but they later eased in the West Bank too.
The future of the West Bank is set to be one of the main issues of the Israeli election campaign.
Gantz, who is running on a centre-right ticket, has hinted that he may be ready to pull back from the territory as part of a peace deal with the Palestinians.
Netanyahu's far-right coalition partners are campaigning for the unilateral annexation of large swathes of the Palestinian territory.
Some 650,000 Israeli settlers live in the West Bank, including annexed east Jerusalem.
The settlements are seen as illegal under international law and a major obstacle to peace, as they are built on land the Palestinians see as part of their future state.