The U.S. State Department is condemning in the strongest terms what it calls the "barbaric attacks" on Christian places of worship in Egypt after bombs at two Coptic churches killed more than 40 worshipers and police officers and wounded about 100 others on Palm Sunday.
The rocket landed in the Eskhol regional council, causing no injuries or damage, Israel's army said.
Israel closed its Taba border crossing to those departing for Egypt after its anti-terrorism office warned of an "imminent" militant attack there.
The closure will remain in effect until April 18, the day after the end of the Passover holiday.
Thousands of Israelis normally travel to Egypt's Sinai for the holiday. Under the closure, Israelis citizens will not be allowed to cross into the Sinai, but will be allowed to return to Israel through the crossing point.
Israel raised its travel warning for Sinai to its highest level, one out of four, signalling "a very high concrete threat", with a travel warning for the rest of Egypt at level three ("basic-level concrete threat").
President Donald Trump is joining in the worldwide condemnation of the church bombings in Egypt, and he says he is "so sad to hear of the terrorist attack" against the US ally.
This was one of the few times the Taba Crossing was shut down since its opening in 1982, following the Israeli-Egyptian peace deal.
The Israeli government statement says that intelligence information shows "increased activity by Islamic State" militants in Sinai.
It adds that with IS losing ground in Iraq and Syria, there is renewed "motivation to carry out terror attacks in different arenas at this time".
Just after 11:30 a.m. on Monday morning, the incoming missile alarm known as a "Code Red" sounded in the Negev's Eshkol region, near Israel's westernmost edge, at the border with Egypt and the Gaza Strip.
But an Egyptian journalist and author of a book on the Islamist insurgency in Sinai, Mohannad Sabry, was cited saying that Egyptian military was capable of controlling the Sinai. However, no organisation took immediate responsibility for the attack.