The Qatar-based broadcaster promised legal action against the decision, saying it aligned Israel with other Arab states that are traditionally its enemies.
On Sunday, Israel's communications minister, Ayoub Kara, accused Al Jazeera of supporting "terroristic journalism" and announced plans to close its Jerusalem bureau, halt its transmissions and revoke its press credentials.
The Israeli Prime Minister Benjamin Netanyahu last month accused Al Jazeera of inciting violence in its coverage of clashes between Muslim worshippers and Israeli security forces at Jerusalem's Al Aqsa mosque.
Kara suggested Israel's plan to block Al Jazeera was inspired by similar moves in Arab countries that are boycotting its main backer, Qatar.
"In the current period, most of the countries in our region have determined that Al Jazeera supports terror, supports religious extremism. These include the Gulf states, including Saudi Arabia, Jordan and Egypt," Kara said in Sunday's press conference.
Kara said he had asked Israel's interior ministry to carry out his requests, but offered no timeline for when he expected the moves to take effect. The proposals would involve multiple agencies and aspects of them require legislation, Al Jazeera reported.
'Odd and biased'
Al Jazeera slammed the decision "made by a state that claims to be 'the only democratic state in the Middle East.'
In a statement, the broadcaster said Israel's explanations were "odd and biased as they are in unison with the actions carried out by a number of Arab countries (Saudi Arabia, UAE, Bahrain, Egypt, and Jordan) that have closed the network's bureaus, shut down its cable and satellite transmissions, and blocked its websites and applications."
On June 5, Saudi Arabia, the United Arab Emirates, Bahrain and Egypt enforced an economic and diplomatic boycott
of the gas-rich emirate, accusing it of supporting terrorism. Qatar has firmly denied the accusations.
The four nations, along with Jordan, closed Al Jazeera's operations in their territories shortly after the boycott began.
Saudi Arabia, the UAE and Bahrain do not recognize Israel as a state, and Israeli citizens are barred from entering their territories.
Shutting down Al Jazeera was one of 13 demands issued to the Qatar as preconditions for ending the boycott. Qatar has said that the list was "made to be rejected."
Last month, the UAE said it sent a letter to the United Nations High Commissioner for Human Rights accusing Al Jazeera of promoting "extremist narratives."
The letter was a response to a statement by the UN Special Rapporteur on the promotion and protection of the right to freedom and expression that denounced demands to shut down Al Jazeera as "a major blow to media pluralism."
Al Jazeera said Israel's claims were groundless. "During the press conference, the minister could not substantiate his comments by referring to a single news bulletin or situation that proved Al Jazeera had not been professional nor objective during its coverage in Jerusalem," said the Al Jazeera statement criticizing the Israeli move.
Al Jazeera said it would continue "covering news and events in the occupied Palestinian territories in a professional and objective manner," and take "necessary legal measures" against the moves to shut it down in Israel.