The closure will remain in effect until April 18, the day after the end of the Passover holiday.
The reported attack came only hours after Israel sealed its border with Egypt following two church bombings on Sunday that killed at least 45 people in northern Egypt.
Israel on Monday closed the Taba Crossing to prevent its citizens from traveling to Egypt's Sinai, citing security threats in the wake of Sunday's deadly twin attacks in Egypt. As was the case in the Egyptian church bombings on Palm Sunday, terrorist elements tend to step up attacks during Jewish and Christian holiday seasons.
Israel Deputy Foreign Minister Tzipi Hotovely said the terrorist attack in Cairo was a reminder that Egypt is also under attack by terrorists, local media reports said.
A military spokesperson confirmed that "a projectile was launched from the Sinai Peninsula", adding that forces are searching the area for the remains of the projectile.
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The decision to close the border and request the return of Israeli citizens was made by Transportation and Road Safety, and Intelligence, Minister Yisrael and Defense Minister Avigdor Liberman.
Last month the bureau issued a similar warning against travel to the Sinai, a popular destination for Israelis over the week-long Passover holiday that starts at sunset today. Instead, Jews eat matzo - unleavened bread - to illustrate how the Israelites had no time to let their bread rise as they fled from bondage in the land of the Pharaohs.
Jihadists have killed hundreds of soldiers and policemen since the military overthrow of Islamist president Mohamed Morsi in 2013 unleashed a bloody crackdown on his supporters.
Israeli authorities warned of "increased activity by Islamic State militants" in Sinai. Egypt has been battling the militants, many linked to the Islamic State group.