The poster announcing the show was cancelled
The free performance at Amnesty International's London offices had been fully booked but on Tuesday Ms Peake announced it was cancelled.
“There was once a theatre that was obliterated. There was a show that did not go on," Ms Peake said.
“Our play is cancelled because art should not be targeted by soldiers or anyone else, in Gaza or anywhere else.
“The show is cancelled. The show must not go on - until we, they, all of us, are free.”
Playwright Ahmed Masoud said: “I am an artist from Gaza and I was shocked by what happened to the only theatre in Gaza. How could a theatre be bombed just like that, without any warning?
“A theatre is not part of a conflict - I cannot stay silent about the bombing of a theatre.”
Ms Peake has previously defended Ken Livingstone when he was engulfed in a row over his comments about Hitler supporting Zionism.
"I think there’s certain issues you have to be very, very careful about," she said.
“I’ve always been very open. I’m very pro-Palestine and anti the occupation but that doesn’t make me antisemitic. Not at all.”