Dozens of members of the Scottish Palestine Solidarity Campaign (SPSC) staged a demo tonight and vowed to continue action until Incubator Theatre production The City was cancelled.
The show, described as a "hip-hop opera", had been due to run at the Underbelly Cow Barn venue in the city's Bristo Square until August 25.
But a spokesman for the Underbelly tonight confirmed that The City had been cancelled.
He said that a protest today had disrupted other nearby Fringe venues and the decision was taken, after the first performance of the show, to close it down at its venue, the Cow Barn in Underbelly Bristo Square.
"We are still trying to find a home for it," a spokesman said, "and it will take a couple of days. The protests were encroaching on other venues and the decision was taken to find a new home for The City."
Insiders at the venue are "very disappointed" by the cancellation.
It is understood Underbelly is committed to the show and will try to find another venue where potential protests do not affect other productions at the Fringe.
The Underbelly statement read: "Earlier today, after discussions between Underbelly, Incubator Theatre, the University of Edinburgh and Police Scotland it was agreed that future performances of The City at the Reid Hall would be cancelled.
"Today's performance of The City went ahead as planned, but the logistics of policing and stewarding the protest around The Reid Hall - and the effect of the disturbance on Underbelly and other venues' other shows - make it untenable for the show to continue in the Cow Barn, Reid Hall.
"Underbelly and Incubator Theatre will work to identify other suitable venues for the show to perform at in Edinburgh.
"All tickets for forthcoming performances of The City in the Cowbarn, Reid Hall will be refunded. When an alternative venue is found, customers will be able to book tickets for that show separately."
Mick Napier, secretary of the SPSC, said before the decision was announced: "The massacre in Gaza is now well into four figures and overwhelmingly that is civilians and a huge number of children.
"Hospitals and schools are being shelled, some repeatedly, and we find that it's unacceptable that an Israeli state-sponsored cultural event should go ahead at the Edinburgh Fringe.
"If the artists were unconnected with the Israeli state we would have no issue with them.
"Our plan is to protest every day and also to use non-violent direct action to prevent it going ahead."
An earlier statement from John Stalker Productions, which is promoting the show, said the Jerusalem theatre company receives an element of arts funding from Israel's Ministry of Culture, among others.
It said: "Incubator Theatre exists to be an agent of significant cultural change in Jerusalem, working in both east and west Jerusalem, and an active force in developing an urban climate of pluralism and openness that accommodates a wide spectrum of opinions and world views.
"This work is of great significance to furthering cross-community dialogue and debate in the region."
Police Scotland said they were aware of the protest.
A force spokesman said: "We respect individuals' right to protest peacefully and our officers will facilitate any demonstration with a proportionate and appropriate deployment.
"This will be balanced against the needs and rights of those impacted by the event and the public can be sure that criminal activity will not be tolerated.
"Police Scotland's priority is to keep people safe and, alongside our partners at the City of Edinburgh Council, we will do our utmost to ensure that performers, spectators, residents and visitors alike are all able to enjoy the Edinburgh Festival to the full."