A government official told Al Jazeera that humanitarian products such as cooking gas, wheat and flour would be allowed to continue crossing into Gaza.
Israeli Prime Minister Benjamin Netanyahu vowed to use a "heavy hand" against the Palestinian militant group Hamas, which dominates Gaza. Israel says it has lost 7,000 acres of forests and farmland to the kite- or balloon-set fires.
The burning kites are part of a Palestinian anti-Israel rally that started on March 30 along the security fence between Israel and eastern Gaza, during which Israeli troops responded with live fire, killing at least 133 Palestinians and injuring 14,000 others.
According to the NGO National Committee to Break the Siege in Gaza, the initiative involves 11 Palestinians, some of them injured by Israeli military and police forces during the last protests in the territory, as well as medical students and patients.
The closure of the Karam Abu Salem border crossing will also affect Gaza's exports, further straining an already crippled economy brought to its knees by the 12-year blockade.
Arabic-language spokesman for the Israeli army, Avichay Adraee, took to social media to reveal that the measures also included reducing Gaza's designated fishing zone from nine to six nautical miles off the coast.
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We've learned from our mistakes, which is the most important thing, and we've made things right", he said. England play Croatia Wednesday night at 7pm.
Netanyahu described the move as a crackdown on the Hamas Resistance Movement.
Only a day earlier, Qatari envoy Mohammed al-Emadi, who has been working behind the scenes to ease tensions in Gaza, suggested in an interview that Palestinians would stop protests and sending incendiary kites if Israel were to ease the siege and allow 5,000 Palestinians from Gaza to obtain work permits for Israel.
"There will be additional steps which I won't detail", he added.
Hamas, which has fought three wars with Israel since 2008, called on the global community to intervene immediately to prevent what it called a "new crime against humanity".
Mahmud Abu Ataya, 25, who recently suffered a leg wound east of Gaza City, said: "I am leaving to be cared for overseas".
In recent weeks, Palestinians in Gaza have been protesting against the naval, aerial and land blockade imposed by Israel and neighboring Egypt since 2006.
Hamas decried Monday's measures as "a new Israeli crime against humanity".
No Israelis have been killed.