"With her death Germany has lost one of the most important voices in its contemporary history," a statement from the foundation said.
German President Frank-Walter Steinmeier said Friedlaender's death "fills me with deep sadness".
"She gave our country the gift of reconciliation, despite everything that the Germans did to her as a young woman," he said. "We cannot be grateful enough" for Friedlaender's efforts.
Friedlaender was born in Berlin into a Jewish family of button makers and trained as a fashion illustrator.
During the Holocaust she was sent to the Theresienstadt camp in what is now the Czech Republic.
While she and her husband Adolf survived and later emigrated to the United States, the rest of her immediate family perished in Auschwitz.
After her husband's death she began taking a memoir-writing class and worked on a documentary about her experiences.
She went back to Germany for the first time in 2003, and moved permanently to Berlin at the age of 88.
Her tireless efforts in keeping the memory of the Holocaust alive, particularly by sharing her experiences with younger people, won her plaudits in Germany and beyond.
Germany's new Chancellor Friedrich Merz joined those paying tribute on Friday, saying Friedlaender had "entrusted us with her story".
"It is our task and our duty to carry it forward," he said.
Steinmeier had been due to award Friedlaender Germany's highest civilian honour at a ceremony earlier Friday, which was abruptly cancelled.
"Until the last, she urged us to defend democracy -- remembering alone is not enough," her foundation said.
Her last public appearance was at a ceremony this week to mark the 80th anniversary of the end of World War II at Berlin's city hall, where she repeated what became her mantra.
"Be human! That is what I ask you to do: be human!" she said.
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