"Al-Jazeera deplores this action from a state that is called the only democratic state in the Middle East and considers what it has done is dangerous," said the official who declined to be named.
He said the broadcaster "will follow up the subject through appropriate legal and judicial procedures".
Israeli Communications Minister Ayoob Kara announced the plan to close Al-Jazeera at a Jerusalem news conference, accusing it of being a "tool" of jihadist Islamic State group, Shiite Iran and its Lebanese ally Hezbollah and the Palestinian Islamist movement Hamas.
Saudi Arabia leads four Arab countries, including Egypt, Bahrain and the United Arab Emirates, which broke ties with Doha in June, accusing it of fostering extremism and who later demanded Al-Jazeera's closure.
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"Al-Jazeera is surprised by the announcement of the Israeli minister of communications in his justification that the decision is consistent with what has been done by Arab countries... Namely Saudi Arabia, UAE, Bahrain, Egypt," the official told AFP in Doha.
The official defended Al-Jazeera's coverage of the Palestinian-Israeli conflict, saying it is "professional and objective" and gives both sides of events.