"I am really sorry to report that we have now received news that Shani Nicole Louk has been confirmed murdered and dead," Israeli President Isaac Herzog told Germany's Bild newspaper.
"What we saw on the Gaza-Israel border goes far beyond a pogrom. We saw a slaughterhouse."
Louk, 23, was one of scores of people taken by Hamas during an assault on the Israeli military and civilian communities that killed 1400 people, mostly civilians.
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," Scholz said during an official visit to Nigeria. "This shows all the barbarism that lies behind Hamas."
Hamas has not commented on Louk's fate.
The circumstances of her death were not immediately clear.
The German government confirmed on Monday (local time) that a German national had died but did not offer specifics.
A family source told Reuters that a part of a body had been found which was matched to Louk's DNA.
Her family initially thought she was alive but injured when she was snatched from the music festival but now believe she was killed on the same day, possibly shot in the head, German broadcaster RTL/ntv said.
"At least she didn't suffer," her mother Ricarda Louk told RTL/ntv.
