In the southern city of Rahat, 100 Palestinians held a rally against the bill, while more than 500 people took part in various demonstrations in the north, police said.
In the northern city of Jisr al-Zarqa, lawmaker Ahmed Tibi of the Arab Joint List called the legislation "a provocation and act of coercion in the place of dialogue and tolerance", a party spokesperson said.
In Gaza, hundreds of supporters of the Palestinain resistance movement, Hamas, that controls the Palestinian territory held a protest march through the Jabalia refugee camp near the enclave's northern border, the New Arab website reported.
Yusef al-Sharafi, a Hamas leader, told the crowd that "this unprecedented Zionist decision is an encroachment on the freedom of Muslims".
"Attempts to ban the Adhan (call to prayer) are doomed to fail because of the steadfastness of the Palestinians," he said, reiterating the long-standing Hamas demand that the Palestinian Authority end its security cooperation with Israel.
The bill, which passed the ministerial committee for legislation on Sunday, had been appealed by Health Minister Yaakov Litzman, who demanded another discussion on it before its first parliamentary reading.
Litzman, a member of the ultra-Orthodox United Torah Judaism party, was concerned that the bill could also outlaw the weekly sirens that indicate the beginning of the Sabbath.
The bill, drafted by Moti Yogev and supported by Prime Minister Benjamin Netanyahu, will now be put on hold until a ministerial committee holds a second vote.