The decision to rescind the offer was made after news of the invitation leaked prematurely, prompting executives to rethink the offer at an emergency meeting of festival executives in Bayreuth on Tuesday night, the Haaretz newspaper said.
"Amid concerns that reactions in Israel would be fiercely negative, the visit was cancelled," the paper wrote.
Calls to the Tel Aviv offices of the Israel Chamber Orchestra on Wednesday were not answered.
The ensemble said on Tuesday it had accepted an invitation to play at the festival next summer despite long-standing Israeli opposition to performing works by the anti-Semitic composer.
"The decision was not to break a taboo," Erella Talmi, the chairwoman of the orchestra's board of directors, told Israeli army radio. "The decision was to accept an invitation that showed a new openness."
But since the Nazi Holocaust, musicians in what is now Israel have largely honoured an unwritten ban on performing pieces by Wagner, Adolf Hitler's favourite composer.
Many Israelis are Holocaust survivors and find the associations provoked by the music distressing.
Writing in the Yediot Aharonot daily on Tuesday, Holocaust survivor Noah Klieger called the orchestra's decision to participate at Bayreuth an "outrageous surrender."
"I have no idea who came up with this idea, but I do know that we must not allow this performance to take place," he wrote.
In 1991, Israeli composer Daniel Barenboim led the Berlin State Opera in a performance of an excerpt from "Tristan und Isolde" in Tel Aviv, prompting catcalls and a walkout by several members of the audience.