Statements by domestic security agency Shin Bet and the police said the three were active members of the Popular Front for the Liberation of Palestine (PFLP), designated a "terrorist group" by Israel, the US and the European Union.
The bomb exploded on August 23 near a spring that serves as a swimming pool close to the Jewish settlement of Dolev, northeast of Ramallah, killing 17-year-old Israeli Rina Shnerb and wounding her father and brother.
"In a joint operation between Shin Bet, the army and the Israeli police, the perpetrators of the... attack have been found and arrested," the domestic security agency and police said in near-identical statements on Saturday.
The statements identified the Palestinians as "residents of the Ramallah area active within the" PFLP.
The PFLP carried out several plane hijackings in the 1960s and 1970s, but has lost traction in recent years in the Palestinian territories.
Shin Bet added that the "cell was preparing other attacks when the arrests occurred, notably gun attacks and kidnappings".
The police said that the arrests of the three had taken place "several weeks ago", without giving specific dates.
Security forces had said the day after the bomb attack that several suspects had been arrested and transferred for further questioning.
No Palestinian group took responsibility for the blast.
Israeli Prime Minister Benjamin Netanyahu on August 26 ordered hundreds of new settler homes to be built near the site of the bomb attack.
Palestinians sporadically attack Israelis in the West Bank, occupied by Israel since the Six-Day War of 1967, but bomb attacks have been rare.
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