Kara claimed that the station was used by militant groups to "incite" violence, accusing the network of "supporting terrorism" and saying that it was "delusional" that Arab states in the Middle East had banned Al-Jazeera for that reason but Israel had not.
The broadcaster "will follow up the subject through appropriate legal and judicial procedures", he added.
According to Al Jazeera, the plan would revoke the credentials of all journalists working for the broadcaster's Arabic and English credentials, shut down its cable and satellite transmissions, and evict staff from their Jerusalem headquarters.
Jordan and Saudi Arabia have recently closed local offices of the Qatar-based news network, while the channel and affiliate sites have been blocked in Saudi Arabia, United Arab Emirates, Egypt, and Bahrain.
Kara said he would ask the Government Press Office to revoke the accreditation of Al Jazeera's journalists in Israel, where it has about 30 staff. Cable and satellite providers have expressed their willingness to turn off its broadcasts, he said.
Al Jazeera's Jerusalem Bureau Chief Walid Omary told Anadolu Agency that no official notification has been received from Israeli part so far. The Al-Jazeera official said yesterday he was "surprised" at Israel's justification, and defended the channel's coverage of the Israeli-Palestinian conflict, calling it "professional and objective". "Here in Israel, there is no place for a channel that backs terrorism either".
Kara also noted that a Saudi Arabia-led alliance that severed ties with Qatar last month had demanded the closing of Al Jazeera among its conditions for ending the dispute.
Netanyahu has, however, frequently criticized news media in general, accusing various outlets of seeking to undermine his government.
The pan-Arab network's offices in the Palestinian territories of Gaza and the occupied West Bank city of Ramallah, however, would not be affected by the current Israeli move.
"If this is not possible because of legal interpretation, I am going to seek to have the necessary legislation adopted to expel Al Jazeera from Israel".
The Foreign Press Association, which represents journalists covering Israel and the Palestinian territories for worldwide news organizations, said the move "is certainly a cause for concern". Under a decades-old agreement, only Muslims are allowed to pray inside the Al-Aqsa mosque compound, although anyone can visit, including Jews.