Three of the killed aid workers were British citizens, WCK said.
The charity said those killed were part of an aid convoy that was leaving a warehouse in central Gaza on Monday.
Israeli Prime Minister Benjamin Netanyahu has acknowledged that Israel’s forces hit “innocent people”.
Gaza’s Hamas-run media office also blamed Israel.
WCK is one of the main suppliers of desperately needed aid to Gaza. It said that it would “be making decisions about the future of [its] work soon”.
According to the charity, the aid convoy was hit while leaving the Deir al-Balah warehouse, “where the team had unloaded more than 100 tons of humanitarian food aid brought to Gaza on the maritime route.”
The convoy was made up of three vehicles, including two that were armoured. The BBC understands that all three were hit in the strike.
WCK said it had co-ordinated the convoy’s movements with the IDF when it was hit.
A Palestinian medical source told the BBC the workers had been wearing bullet-proof vests bearing the WCK logo.
The Palestine Red Crescent Society said it had recovered all seven bodies from the scene of the incident following a “challenging operation spanning several hours”.
The humanitarian group added that the bodies had been taken to the Abu Yousef al-Najjar hospital in southern Gaza in preparation for their evacuation through the Rafah border crossing into Egypt.
Mr Netanyahu released a video message on Tuesday in which he said Israeli forces were behind the attack.
“Unfortunately, in the last 24 hours there was a tragic case of our forces unintentionally hitting innocent people in the Gaza Strip,” he said.
“It happens in war, we check it to the end, we are in contact with the governments, and we will do everything so that this thing does not happen again.”
The IDF had earlier said it was conducting a thorough review at the highest level to understand the circumstances of the “tragic incident”.
“We will get to the bottom of this and we will share our findings transparently,” IDF spokesperson Rear Adm Daniel Hagari vowed.
“The work of WCK is critical; they are on the frontlines of humanity.”
Mr Hagari added that the IDF had been “working closely with the World Central Kitchen to assist them in fulfilling their noble mission of helping bring food and humanitarian aid to the people of Gaza”.
According to WCK, the workers who died were Australian, Polish, British, Palestinian and a dual US-Canadian citizen.
“I am heartbroken and appalled that we – World Central Kitchen and the world – lost beautiful lives today because of a targeted attack by the IDF,” the charity’s chief executive Erin Gore said in a statement.
“The love they had for feeding people, the determination they embodied to show that humanity rises above all, and the impact they made in countless lives will forever be remembered and cherished.”
According to Cogat, the Israeli defence ministry body in charge of co-ordinating aid deliveries to Gaza, the charity is responsible for 60% of the non-governmental aid getting into the territory.
WCK said in a recent statement that it had served more than 42 million meals to people in Gaza since October and had been ready to provide more than one million more.
The charity recently made headlines for providing hundreds of tonnes of food for Gazans that was transported on the first aid ship in March.
Aid agencies have started delivering aid by sea in order to increase the amount getting into the territory, which the UN says is on the brink of famine.
But following the deadly strike, a second US-based charity, the American Near East Refugee Aid (Anera), which was working closely with WCK, told the BBC it was also freezing its operations in Gaza.
Australian Prime Minister Anthony Albanese has confirmed that aid worker Lalzawmi “Zomi” Frankcom was among those killed and has offered his condolences to family and friends.
In a statement, he said: “This is someone who was volunteering overseas to provide aid through this charity for people who are suffering tremendous deprivation in Gaza. And this is just completely unacceptable.”
He said Australia expected “full accountability”, adding that it was a “tragedy that should never have occurred”.
Wojciech Bakun, the mayor of the Polish city of Przemysl, said that Damian Soból, who was from the area, was also among those killed.
Mr Bakun described Mr Soból as a “fantastic boy”, adding that no words could describe the feelings of those who knew him.
The Polish foreign ministry said it had received reports of the incident and was seeking urgent official confirmation from the Israeli government about the victim’s identity.
“We extend our deepest condolences to the family of the Polish volunteer who was providing aid to the Palestinian people in the Gaza Strip,” it wrote on X, formerly Twitter.
The UK Foreign Office said it was aware of reports of the death of a British national in Gaza and was urgently seeking further information.
UK Foreign Secretary Lord Cameron wrote on X that British nationals were reported to have been killed and that officials were urgently seeking to verify this.
“We have called on Israel to immediately investigate and provide a full, transparent explanation of what happened,” he wrote.
The Palestinian killed in Monday’s strike has been named as Saif Abu Taha – the driver of one of the cars in the convoy that was struck.
Adrienne Watson, a spokesperson for the White House National Security Council, said on X: “We are heartbroken and deeply troubled by the strike that killed [WCK] aid workers in Gaza.
“Humanitarian aid workers must be protected as they deliver aid that is desperately needed, and we urge Israel to swiftly investigate what happened.”
More than 196 aid workers have been killed in Gaza since October, according to the US-funded Aid Worker’ Security Database, which records major incidents of violence against aid personnel. Not all have been killed in the line of duty.
Much of the Gaza Strip has been devastated during the Israeli military operations that began after Hamas gunmen attacked southern Israel on 7 October, killing about 1,200 people and seizing 253 hostages.
About 130 of the hostages remain in captivity, at least 34 of whom are presumed dead.
More than 32,916 people have been killed in Gaza since then, the Hamas-run health ministry says.
