The Israeli move is important because that agreement, which has been a pillar of the Jewish state's security policy for more than three decades, prohibits any major Egyptian military presence in the vast expanse of desert and mountains that forms a deep buffer zone between Israel and the Nile Delta, the Egyptian heartland.
Monday's authorization by Prime Minister Binyamin Netanyahu's coalition government follows an increase in violence in Sinai against Egyptian security forces and civilians by militant groups following the Egyptian army's dismissal of Islamist President Mohamed Morsi July 3.
Most of the groups are aligned with al-Qaida and are largely equipped with arms smuggled from Libya, battered by rival militias and awash with weapons since the toppling of Moammar Gadhafi in an eight-month civil war that ended in October 2011.
The Sinai attacks included the ambush Monday of a bus carrying workers to a cement factory owned by Egypt's armed forces near the coastal city of El Arish, capital of northern Sinai.
Three workers were killed and 17 wounded in a barrage of rocket-propelled grenades, security officials reported.
Sinai has been pretty much out of control since the toppling of dictator Hosni Mubarak in a pro-democracy uprising Feb. 11, 2011.
But since Morsi's downfall, the violence has intensified, with at least 11 security officials assassinated since July 3 and several security bases and checkpoints attacked.
"The people who're attacking the checkpoints are the supporters of Morsi who're against him leaving office," said a senior security official in El Arish.
"These are armed gangs that are getting their weapons from outside sources and sources within Egypt."
Authorities in Cairo are concerned the jihadists' depredations will spill over into Egypt proper on the west bank of the Suez Canal and ignite Islamist violence across the country, pitting Morsi's supporters not just against the military but against Egypt's large Coptic Christian minority.
Israel fears that if the Egyptian military cannot contain or crush the Muslim extremists in Sinai, the militants will launch a new wave of attacks on the Jewish state that could threaten the 1979 peace treaty, the first signed by Israel with its Arab adversaries.
With Israel's northern frontier with Syria in turmoil because of the 28-month-old civil war there, and the fragile stability of neighboring Jordan, with which Israel signed another peace pact in October 1994, increasingly under threat, Netanyahu and his generals are deeply concerned that the relative stability that has existed in the region is now in danger.
The Egyptians are poorly equipped to counter a major escalation of violence by Islamist militants, particularly one that spreads eastward across the canal.
Its 310,000-strong army and the air force, equipped with U.S.-supplied F-16 fighters and more than 1,000 M1A1 Abrams main battle tanks, are configured to fight conventional armies, not the estimated 1,000 elusive Islamist fanatics able to move around Sinai's 23,600 square miles of desolation.
Mubarak crushed Islamist insurgents in the 1990s with great ferocity, but even moderate Islamists have been incensed by the army's overthrow of Morsi, a leader of the once-banned Muslim Brotherhood and Egypt's first democratically elected president.
Sinai was always a security weak spot for Egyptians, but the problem's been intensified over the last couple of years by the unification of jihadist groups in the Hamas-ruled Gaza Strip which adjoins Sinai.
In June 2012 they announced the formation of an umbrella group, the Mujahideen Shura Council in the Environs of Jerusalem, linked to al-Qaida.
By moving into Sinai, the jihadists, instead of operating along Gaza's 25-mile border with Israel, now can mount attacks along the Jewish state's 160-mile border with Sinai.
Until Morsi was toppled, their main objective was fighting Israel. Now they're taking on the Egyptian army as well.
That may provide Israel with a breathing space. But it will mean allowing much larger Egyptian forces into Sinai, and that could cause some jitters.
Israelis may even have to pitch in themselves to eradicate the jihadists, a ground-breaking prospect, but one fraught with political dangers.