It follows a decision last month by al-Jazeera's owners, the state of Qatar, to cut trade ties with Israel.
The work visas of some al-Jazeera employees based in Israel will not be renewed, according to reports.
Al-Jazeera's journalists will have limited access to Israeli news conferences and briefings.
Qatar was the only Gulf state to have trade ties with Israel, but they were cut in January in protest at the Israeli offensive in Gaza.
Israeli officials were fiercely critical of al-Jazeera's coverage of the conflict in Gaza, accusing it of being a mouthpiece for the militant Islamist movement, Hamas.
An Israeli official in Jerusalem was quoted as saying that it was Qatar's own actions which had now created a problem for al-Jazeera.