The Shin Bet internal security agency said the youths were detained after a June 10 attack in the village of Yafia near the northern Israeli city of Nazareth.
"Three Jewish minors have been arrested for having set on fire a vehicle in the village of Yafia... And for having sprayed graffiti calling for vengeance after the attack on the Sarona in Tel Aviv," it said in a statement.
On June 8, two Palestinians shot dead four Israelis at the Sarona Market, a popular Tel Aviv nightspot.
Shin Bet said the minors "were preparing an attack in response to attacks carried out recently by Palestinians. But after the Tel Aviv attack, they decided to act".
Two of the suspects are residents of northern Israel while the third is from a Jewish settlement in the occupied West Bank, said Shin Bet.
They are expected to be indicted in the coming days, it added.
Israel has seen a wave of "price tag" attacks -- a euphemism for Jewish nationalist-motivated hate crimes targeting Palestinians and Arab Israelis and their property, as well Muslims and Christian holy sites.
The boy's parents later died of their injuries.
Two Israelis were charged in January over that arson attack.
In April, Israeli prosecutors charged seven young Jews -- including a soldier and two minors -- in connection with a wave of "price tag" attacks between 2009 and 20013 and in the second half of 2015.
The attacks included torching an inhabited Palestinian home and beating a Palestinian man with sticks, the Israeli justice ministry said.
