The City, by Incubator Theatre, has failed to find an alternative venue and will now not be run at all at the Fringe this year.
It was due to be staged by the theatre group, who receive funding from the Israeli government, at the Cow Barn in Underbelly in Bristo Square but the protests, which disrupted other venues, led to its cancellation.
A statement from Underbelly said: "Underbelly and Incubator Theatre have worked very hard to find an alternative venue for The City.
"We are very disappointed to announce that unfortunately we have been unable to find a space that is viable for the show and for the security of the audience.
"A private performance for friends took place today but otherwise all performances at Underbelly of the show are now cancelled."
More than 1,460 Palestinians, mostly civilians, including many children, have died in the latest conflict in Gaza, as well as 63 Israelis, mostly soldiers.
Scots Makar Liz Lochhead was among the signatories of an open letter protesting against the staging of The City last month.
The letter, also signed by figures such as playwright David Greig, author and artist Alasdair Gray, and theatre directors Ben Harrison, Graham McLaren and Cora Bissett, called for the Underbelly venue to reconsider staging the group's opera.
The letter said: "The current, brutal assault by Israel upon the people of Gaza, which is an appalling collective punishment, underlines the seriousness of your error in co-operating with a company which is funded by the Ministry of Culture of the state of Israel."
A Scottish Government spokeswoman said: "The Scottish Government has repeatedly stated on this issue that it does not tell individual venues or galleries what they can or cannot programme. We have made clear the Scottish Government's position on the crisis in Gaza. We have called for an embargo on UK arms exports to Israel and have repeatedly called for an immediate and unconditional ceasefire to put an end to the violence. We have offered medical help, pledged to accept refugees and are providing £500,000 to help people affected by the crisis."
The Edinburgh Festival Fringe Society said: "The Edinburgh Festival Fringe is underpinned by our open access principles. These principles guarantee artists the freedom to present their work to the public without the intervention of a curator or the need for official approval. We are therefore deeply saddened when any artist or show is prevented from taking part in the Fringe. We have done what we can to support Underbelly and Incubator Theatre as the situation has developed and we respect the difficult decisions that they have taken.
"To be clear, our commitment to freedom of expression means that we support the right of all participants of the Fringe and members of the public to hold and express differing political views, but we also believe in an artist's right to freedom of expression, and that the curtailment of this freedom is contrary to the fundamental ethos of the festival."