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The family were informed of her death by the Israeli military.
“It is with great sadness that we announce the death of my sister,” her sibling Adi Louk said on social media.
Ms Louk's mother, Ricarda Louk, told NTV: “Unfortunately, we received the news yesterday that my daughter is no longer alive.”
She said her daughter’s body had not yet been found, but some remains were submitted for a DNA test.
The family previously expressed their hope that she was alive, but now believe she was killed on the same day as the attack, NTV reported.
“At least she didn't suffer,” her mother said.
Ms Louk’s father, Nissim Louk, said she and her friends tried to escape the attack in their car but 10 minutes later, they were met by armed Hamas militants who shot at the vehicle, killing his daughter “instantly”.
Her death was confirmed by Israel's Ministry of Foreign Affairs in a post on X.
It said she was “paraded around Gaza” by Hamas. “Our hearts are broken,” the ministry said.
German Chancellor Olaf Scholz, whose government has staunchly supported Israel as it mounted an offensive against Gaza in retaliation, said Hamas had to be held accountable.
“For me, this news is terrible,” Mr Scholz said during an official visit to Nigeria. “This shows all the barbarism that lies behind Hamas.”
Ms Louk had been attending the Supernova music festival near Kibbutz Re'im, in southern Israel, when she was kidnapped.
Images seen in the aftermath of the attack showed her lying in the back of a pick-up truck as it was being driven back to Gaza.
The student from Berlin was on holiday in Israel when she attended the event close to the border with Gaza.
Authorities believe more than 220 people were taken hostage by Hamas, with at least four having been released following negotiations.