The dead man was named as Mohammed Shwikani, a 20-year-old militant with the armed wing of Islamic Jihad, the group said.
The Israeli military said the strike targeted a rocket-launching squad following an evening in which armed groups fired 25 rockets at southern Israel.
"A short while ago, the IDF (army) targeted a rocket launching squad in the northern Gaza Strip moments after it fired rockets towards southern Israel. A direct hit was confirmed," a military statement said.
"Over the past few hours, 25 rockets fired from the Gaza Strip hit southern Israel," it added.
Earlier on Saturday, violence flared along the border east of Gaza City when militants fired an anti-tank missile at an Israeli jeep, wounding four soldiers.
In response, Israel fired a barrage of artillery fire and shells, killing three people and injuring 25, five of them seriously, medical officials and witnesses said.
One of the injured died later in hospital.
Ashraf al-Qudra, spokesman for the Hamas-run health ministry said some of the injured were in "serious to critical condition," adding the dead and the wounded appeared to be civilians.
Witnesses said the shooting took place after an anti-tank missile slammed into the Israeli jeep near the Karni crossing east of Gaza City, in an attack claimed by the armed wing of the left-leaning Popular Front for the Liberation of Palestine (PFLP).
The Israeli army confirmed that four soldiers had been wounded by an anti-tank missile.
Military sources said two of the soldiers were in serious condition.
Medics also said five Palestinians were wounded in another instance of Israeli shelling near Khan Yunis in southern Gaza.
-- Threats of revenge --
Late Saturday, Israeli Prime Minister Benjamin Netanyahu held talks with his Defence Minister Ehud Barak and Chief of Staff Lieutenant General Benny Gantz "to discuss the situation in the south," the premier's official Twitter account said.
"The IDF responded severely to the incident and additional responses will be examined in the coming days," Barak was quoted as saying in a statement from his office.
The bloodshed was swiftly condemned by Gaza's Hamas government, as well as by militant groups which vowed revenge.
"The occupation attacked Palestinian civilians east of Gaza City and Khan Yunis. We consider this escalation as very dangerous. It must stop immediately," said Hamas spokesman Fawzi Barhum.
The armed wing of the radical Popular Resistance Committees also released a statement vowing that "the Zionist enemy will pay a high price for this crime against Gaza."
And Islamic Jihad also issued a warning, saying: "Every aggression against the Palestinian people will be followed by a response from the resistance."
In recent days, tensions have been rising between Israeli troops and Gaza militants.
On Thursday, an Israeli soldier was wounded near the border east of Khan Yunis when a tunnel packed with explosives was detonated in an attack claimed by Hamas's armed wing, the Ezzedine al-Qassam Brigades.
Several hours earlier, a 13-year-old Palestinian was shot dead by gunfire from an Israeli helicopter in the same area, medics and witnesses said.
And on Tuesday, three Israeli soldiers were wounded in an another explosion in the same area.
An earlier flare-up in and around Gaza began on October 22 and continued for three days, with eight militants killed in Israeli air strikes, and armed groups firing more than 100 rockets across the border, severely wounding two Thais.
In December 2008, just six weeks shy of general elections, Israel launched a huge operation in Gaza to stamp out Palestinian cross-border rocket fire which cost the lives of 1,400 Palestinians -- half of them civilians -- and 13 Israelis, 10 of them soldiers.