Ashraf al-Qudra, the spokesman of the Gaza-based health ministry, told reporters on Friday that Mohamed Abu Saada, 26, was killed and three others were injured by Israeli gunfire.
In Gaza, which has been under an Israeli siege since 2006, hundreds of supporters of the Islamist Hamas group that controls the Palestinian territory held a protest march through the Jabalia refugee camp near the enclave's northern border.
Abu Sa'ada was shot with a live round in his chest, causing instant death, while another young man was shot with a gas bomb in his chest and a third in the leg.
The Israeli army said that "during a violent riot adjacent to the security fence in the central Gaza Strip, dozens of rioters breached the buffer zone, approached and damaged the security fence and attempted to infiltrate Israel". Speaking at the rally, Hamas lawmaker Yousef Al-Sharafi called the bill a provocation against Muslims.
It said forces at the scene fired warning shots in the air to disperse them and that it is investigating the incident.
Around 17.5 percent of the population in Israel are Palestinian Muslims who remained in their lands during the Israeli occupation in 1948, but they complain of discrimination and are under-represented in high-level jobs.
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.
Palestinian youths have been holding protests near the Gaza border fence every Friday over the past year.
The bill was originally put forth by Habayit Hayehudi MK Moti Yogev and had been meant to prevent the broadcasting of nationalistic messages and incitement over mosque loudspeakers.
Although the legislation supported by Israeli Prime Minister Benjamin Netanyahu will concern not only mosques but all religious institutions, it is perceived by the Palestinian community as an encroachment on their rights.
While the draft bill applies to all houses of worship, it is seen as specifically targeting mosques.