Israel's border closure comes one day after attacks on two Coptic Christian churches in Egypt Sunday left 36 people dead.
As Israel reacted to the bomb blasts, a rocket fired from the Sinai region landed in southern Israel.
"The fighters of the Islamic State have bombed the Jewish settlement in southern Palestine with a Grad rocket", Sinai Province declared in a statement.
Until at least April 18, the directive said, Israel will not permit its citizens to enter the Sinai through the Taba crossing; Israelis now on the peninsula can return to Israel.
Many Israeli nationals have already crossed through over the past few days, and others were expected to enter Egypt on Monday.
The projectile hit a greenhouse landing in a non-residential area, the Israel Defense Forces (IDF) said.
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").
The bureau cited, "further escalation in the severity of the threat posed to Israelis visiting Sinai and its immediate surroundings".
IS claimed responsibility for the attack shortly after. Ironically, many see Passover as an opportunity to vacation in Egypt.
Islamic terrorists launched rockets Monday morning, on the eve of Passover, from the Sinai towards southern Israeli communities in the Eshkol Region. 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.
The Egyptian military is reported to have carried out a number of air strikes in the terror-ridden peninsula on Monday.
But Israel has urged its citizens to avoid the area in recent years because of Islamic militant activity.
"Israel sends condolences to the families of those who were murdered in yesterday's terrorist attacks in Egypt, and wishes for a quick and full recovery to the wounded", a government statement read.