The bill, supported by 48 against 41 of the Knesset's 120 members, seeks to "defend (Israel's) status as a Jewish and democratic state", said Avi Dichter, the bill's sponsor, of the ruling Likud party.
On Sunday, ministers gave the bill the initial green light.
It needs to be debated by a parliamentary committee and voted on three more times in the plenum before it becomes part of the country's so-called "basic laws", which are similar to a constitution.
It would give special status to the "Jewish and democratic" nature of Israel, to the Jewish calendar and to Hebrew as Israel's official language.
The bill's explanatory notes said such legislation was "especially crucial in times like these, when there are those who seek to undermine the Jewish people's right to a national home in its land".
Some 17.5 percent of Israel's population are Arab, and are descendants of Palestinians who remained after Israel's creation in 1948.
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Public signs and government services are typically in Arabic as well as Hebrew, but it was unclear if the new bill would change that.
Prime Minister Benjamin Netanyahu's government is seen as the most right-wing in the country's history, and Arab Israelis allege widespread discrimination.
Defining Israel as the "national home of the Jewish people" has also raised concerns among rights activists and others worried over discrimination and attempts to further mix religion and state.
"No apartheid law, as racist and nationalistic as it may be, will erase the fact that two peoples live here," parliament member Ayman Odeh, who heads the mainly Arab Joint List alliance, said.
"The extreme right-wing government is trying to spark a fire of nationalistic hatred, but I still believe there lives a majority here that wants to live in peace, equality and democracy", he said.
Masud Ganaim, of Odeh's list, questioned the need to legislate the principles that already appear in Israel's Declaration of Independence, accusing the bill of being an attempt to target Arabs.
Dichter, however, rejected claims that the law would harm Arabs or the Arabic language, saying in the debate ahead of the Wednesday vote that Hebrew would be the national language but Arabic would have a "special status".