The ongoing kite and balloon attacks have burned thousands of dunams of forests and agricultural land adjacent to the Gaza border in recent months.
It is not believed any Israeli soldiers were hurt in the shooting.
More than 130 Palestinians have been killed by Israeli fire since the protests began on March 30.
The Hebrew-language official Israeli TV reported that "it would be different if Hamas responds with shells or rockets".
Israel has not officially confirmed the cessation of hostilities.
The soldier was the first to be killed on the Gaza front in active duty since a 2014 war between Israel and Hamas, an Israeli army spokesman said.
The IDF jets launched "wide-scale" airstrikes at targets in the Gaza strip, killing a total of four Palestinians - one protester and three Hamas fighters - and injuring at least 120.
The Israeli army said they struck 60 Hamas sites including weapon manufacturing sites, a drone warehouse and a military operations room.
"With Egyptian and United Nations efforts it has been agreed to return to the era of calm between (Israel) and Palestinian factions", Hamas spokesman Fawzi Barhoum told Reuters late on Friday.More news: Wimbledon 2018 -- Kevin Anderson wins men's semifinal match
In response to Israel's "massive" wave of airstrikes, activists began circulating the #StoptheWar hashtag in an effort to pressure the worldwide community to step in and stop Israel's efforts to launch yet another catastrophic assault on the "occupied, blockaded, unlivable, and exhausted Gaza Strip".
Protesters gather while burning tires near the fence along the Gaza Strip's border with Israel east of Khan Younis on Friday.
Al Aqsa Radio, a Gaza station, said the Palestinians broke into an Israeli army post, vandalized it, seized military equipment, then returned to Gaza.
Earlier at least four Palestinians were killed on Friday by Israeli forces near the Gaza-Israel fence, according to Gaza's Health Ministry officials.
Palestinians are demanding the right to return to homes and villages they fled or were driven from during the conflict surrounding the creation of the modern state of Israel in 1948.
There were no reports of injuries in that strike and there was no major Israeli bombing campaign overnight or mortar fire from Gaza toward Israel.
Last weekend saw the most severe exchange of fire in Gaza since a 2014 war.
"Any reasonable person who sees the... farmland that has been scorched [by incendiary kites and balloons] understands the intolerable nature of the situation", he told a group of Israelis living near the Gaza-Israel buffer zone.
Prime Minister Benjamin Netanyahu of Israel and his defense minister, Avigdor Lieberman, arrived at military headquarters in Tel Aviv on Friday night for emergency meetings with top officials, a highly unusual event for the start of Sabbath.