Herzog, who holds a largely ceremonial post, made the call following spontaneous demonstrations in Tel Aviv overnight in response to the minister's dismissal.
"For the sake of the unity of the people of Israel, for the sake of the necessary responsibility, I call on you to halt the legislative process immediately," Herzog said in a statement.
The plan to hand more control to politicians and diminish the role of the Supreme Court has ignited months of protests and been questioned by Israel's top allies including the United States, which expressed concern Sunday.
Netanyahu's hard-right government argues the changes are needed to rebalance powers between lawmakers and the judiciary.
Yoav Galant, the former defence minister and staunch ally of Netanyahu, earlier broke ranks and called for a halt to the reforms -- with lawmakers scheduled to vote this week on a central part of the proposals, which would change the way judges are appointed.
"The growing social rift has made its way into the (army) and security agencies," said Galant, a member of Netanyahu's right-wing Likud party. "It is a clear, immediate and tangible threat to Israel's security.
"I am committed to Likud values... and placing the State of Israel above all... but major changes on the national level must be made through deliberations and dialogue," he added, calling for a halt to the protests.
On Sunday, moments after Netanyahu sacked Galant, demonstrators seized a central highway cutting through the coastal city of Tel Aviv, blocking traffic and burning tyres.
Some threw metal barricades at mounted offices while police deployed water cannon.
The large crowd waved national flags, blew airhorns and chanted in Hebrew: "Israel is not a dictatorship" and "No to a fascist government!"
"Last night we witnessed very difficult scenes," Herzog said.
"The entire nation is rapt with deep worry," he added, in an appeal to the government. "Our security, economy, society - all are under threat."
After months of rallies against the reform, including a weekend demonstration that brought out an estimated 200,000 people in Tel Aviv, protesters in the city said it felt like "a sort of climax".
In Jerusalem, demonstrators gathered Sunday outside the prime minister's residence, while other rallies took place in the northern city of Haifa and Beer Sheva in the south.
Protesters have announced a "national paralysis week", including protests outside ministers' homes and parliament.
The United States said it was "deeply concerned" and called on Israeli leaders to reach a compromise.
The White House noted that President Joe Biden recently told Netanyahu that "democratic values have always been, and must remain, a hallmark of the US-Israel relationship".
Galant, a former general, was named to his post in December as part of Netanyahu's coalition with extreme-right and ultra-Orthodox allies.
Two other Likud lawmakers have voiced support for Galant, raising questions over whether the government could count on a majority if it pushes ahead with a vote.
Adding to the political uncertainty, Israel's consul general in New York, Asaf Zamir, tendered his resignation Sunday over Netanyahu's "dangerous decision".
Opposition leader Yair Lapid said that while the prime minister had sacked Galant, "he cannot fire reality and cannot fire the people of Israel who are standing up to the insanity of the coalition".
"The Prime Minister of Israel is a danger to the security of the State of Israel," Lapid added.
A parliamentary committee has amended the draft law to make it more acceptable to opponents, but the opposition has ruled out backing any part of the reform package until all legislative steps are halted.
Netanyahu, in a televised address last week, vowed to "responsibly advance" the reforms and "end the rift" they have caused.
In response, Attorney General Gali Baharav-Miara on Friday accused Netanyahu of "illegal" public intervention on the process of adopting the judicial reforms.
Netanyahu is on trial over charges of bribery, fraud and breach of trust, which he denies.
His broadcast gave rise to contempt of court accusations filed with the Supreme Court by the Movement for Quality Government in Israel, an anti-corruption campaign group.
The group's complaint alleges Netanyahu violated a court ruling that an accused prime minister does not have the right to act in a matter that could constitute a conflict of interest.