Zouheir Bahloul, 67, branded parliament "racist" and "destructive" for passing the law, which also puts Hebrew above Arabic as the official language.
"[The law] removes the Arab population from the path of equality in Israel," he told Israeli TV network Reshet.
The bill passed on 19 July, provoking anger from Israel's Arab minority.
Arab members of the Knesset tore up copies of the bill and shouted their disgust, before some were thrown out of the chamber.
"I am resigning from the Knesset," Mr Bahloul, a member of the opposition Zionist Union party, said on Saturday.
"Should I sit on the fence? Should I give legitimacy to this destructive, racist, extremist parliament?"
He added that he could not face telling his grandson that he had kept his seat in the Knesset.
After the bill was passed, Israel's Prime Minister Benjamin Netanyahu praised it as a "defining moment" in the country's history.
"A hundred and twenty-two years after [the founder of modern Zionism Theodore] Herzl made his vision known, with this law we determined the founding principle of our existence," he said.
Called The Basic Law: Israel as the Nation State of the Jewish People, the legislation essentially defines Israel first and foremost as a Jewish state.
It was created because some Israeli Jewish politicians consider the founding principles of Israel's creation, as a state for Jews in their ancient homeland, to be under threat.
But Israeli Arabs, who comprise about 20% of the country's population, see it as evidence that Israel is downgrading their status.
They have equal rights under the law but have long complained of being treated as second-class citizens and say they face discrimination and worse provisions than Israeli Jews.
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