The bill received a preliminary approval from a three-quarters majority vote in the Israeli parliament and but is yet to pass a further two readings before it becomes law.
Israeli prime minister Benyamin Netanyahu urged the Knesset to vote for the bill.
"This law is meant to suspend from the Knesset those MKs who stand behind terror," Netanyahu said.
The legislation is primarily aimed at elected Palestinian-Israeli lawmakers such as outspoken MK Hanin Zoabi, and may have them suspended from the Knesset for dissent.
"Netanyahu is quietly stealing Arab members' right to a democratic discourse," Israeli-Arab legislator Zouheir Bahloul said.
"Today this law is being promoted to harm the Arab MKs, whose statements and actions do not find favour with the political majority," the Association for Civil Rights in Israel said.
"Tomorrow, it may harm other MKs who express opposing position to that of the ruling consensus," the rights group added.
The Israeli parliament already has the power to censure its members.
|Last month, three Palestinian MKs were suspended from speaking in Knesset as a "punishment" for supporting the families of Palestinians killed by Israeli forces|
Punishing pro-Palestinian dissent
Last month, three Palestinian MKs were suspended from speaking in Knesset as a "punishment" for supporting the families of Palestinians killed by Israeli forces and whose bodies remained with Israeli authorities.
Jamal Zahalka, Hanin Zoabi and Basil Ghattas had joined a meeting with a Palestinian committee to pressure authortiies to hand over the bodies of the victims to their families for burial.
But Israeli officials confirmed on Monday that the prime minister has refused to return the bodies of Palestinians killed by Israeli fire.
Netanyahu has long been accused of prejudice by many of Palestinians living in Israel, who make up about 20 percent of its 8.4 million population.
Last year, the Israeli prime minister drew global outrage for comments he made in attempt to win voters on election day.
In a video posted on Facebook during polling, Netanyahu warned that the rule of the right-wing is "in danger" because "Arab voters are going to the polls in droves."
He later drew back his comments in an apology deemed "not sincere" by Israel's Palestinian community.