The two had reaffirmed their commitment to working together to fight radical groups such as the Islamic State group.
The restrictions will reportedly be in force until April 18 which marks the end of the major Israeli holiday Passover and will not concern the foreign nationals.
Monday morning ISIS claimed responsibility for a rocket attack that landed in landed in a greenhouse in the southern Eshkol Regional Council on Monday, according to ISIS linked news agency Amaq.
In its statement, the Israeli government said their intelligence indicates "increased activity" by the Islamic State in Sinai and a "desire to commit terrorist attacks against tourists in Sinai, including Israelis, in the immediate term".
Egypt's army-backed authorities say they are battling the Welayat Sinai ("Province of Sinai") group, which is alleged to have links with the Daesh terrorist group.
Israel closed its border crossing to the Sinai peninsula Monday amid fears that a terrorist attack was "imminent", a day after twin bombings rocked Coptic Christian churches in Egypt. "In light of the gravity of the threat, the anti-terror bureau advises Israelis now in the Sinai to leave immediately and return to Israel".
Egypt is waging a military campaign against Islamist extremist militants in the Sinai, who have been behind attacks on Egyptian civilians and soldiers as well as periodic rocket fire into Israel. It adds that with the Islamic State group losing ground in Iraq and Syria, there is renewed "motivation to carry out terror attacks in different arenas at this time".
The weeklong festival is widely celebrated in Israel even among otherwise nonreligious Jews.
Ironically, many Israelis like to visit the Sinai during Passover, a holiday marking the Jewish people's departure from Egypt thousands of years ago, as chronicled in the Bible.
Leavened goods like bread and items made from yeast such as beer are banned during the holiday.