Israel's Iron Dome system shot down at least two rockets, the military said.
Israeli gunfire has killed more than 220 Palestinians since the start of the demonstrations, which have included breaches of Israel's border fence.
Palestinian officials said that in addition to Baraka, five other Hamas men and a member of the Popular Resistance Committees were killed.
Israel's army is warning of rockets fired from the Gaza Strip after a Hamas commander allegedly was killed in a Gaza raid that also left one Israeli officer dead. He was identified as Nour Baraka. These are complicated operations and require a great deal of courage by the elite soldiers who sneaked into Khan Younis, and, after they were "burned", faced a long and hard path back home.
The Israeli military said there had been an exchange of fire during an operation in Gaza, with troops withdrawing from the territory with the help of aircraft.
"At this incident, an IDF officer was killed and an additional officer was moderately injured", it added, referring to the Israel Defence Forces.
The military wing of Hamas movement issued a statement in which it mentioned the details of the Israeli aggression, clarifying that its fighters clashed with the Israeli occupation force east of Khan Younis after discovering their secret presence (boarded a civilian car).
An Israeli ground operation to kill or abduct militants inside the Gaza Strip would be rare. The Israeli military chief, Lt. Gen. Gadi Eisenkot said a "special force" carried out "a very meaningful operation to Israel's security", without elaborating.
Oil tanker and frigate collide off Norway, 7 injured
It is unclear what caused the collision but several oil and gas terminals were shut down as a precaution. Firefighters have also confirmed the frigate is listing as it takes on water.
Violence has flared regularly along the Israel-Gaza border since Palestinians began protests there on Mar 30 to demand rights to land lost to Israel in the 1948 war of its creation.
At the weekend, Israel allowed the transfer of a reported $15 million in cash to the Gaza Strip from Qatar, partly for the payment of wages to government employees.
Earlier Sunday, Netanyahu had defended his decision to allow the transfer of the Qatari money, rejecting criticism that the move had strengthened the Islamic militant group.
Benjamin Netanyahu told reporters he was committed to restoring quiet along the Israel-Gaza frontier and preventing a humanitarian crisis in the coastal Palestinian territory.
Israel and Palestinian militants in Gaza have fought three wars since 2008, and recent months of unrest have raised fears of a fourth.
Others have died in tank fire or air strikes.
More than 170 demonstrators, most unarmed, have been killed by Israeli army fire in the confrontations in which some of the participants threw stones, burned tires or threw grenades toward Israeli forces.
The enclave with almost two million people has been under an air and sea blocakde imposed by Israel since 2007. It is the first installment of $90 million that Qatar has pledged to cover the salaries of thousands of unpaid Hamas employees for six months.
"Thanks to the heroes who work year-round in the shadows to ensure Israel's security, we can all live here safely", said Naftali Bennett, leader of the Jewish Home party and a member of the security cabinet who has criticized Liberman's response to months of ongoing violence on the Gaza border.