Scots Makar Liz Lochhead is among the signatories protesting against the staging of The City by Incubator Theatre, a company partially funded by Israel's Ministry of Culture.
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 hip-hop opera.
The letter says: "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."
However, Ms Hyslop said: "The Scottish Government share the public's concern of what is happening in Gaza, and we have offered humanitarian support for the victims. In terms of cultural boycotts, I strongly believe in the freedom of expression, and I don't believe cultural boycotts are consistent with the rights of artists to the freedom of expression.
"This company can speak for itself, in terms of its relationship with the Israeli government and the venue can take responsibility for the production, but I believe we have to be careful about restricting any artist, from any place."
Leading Scottish composer James MacMillan is also against the ban, saying on Twitter: "I would like to publicly support the Fringe in promoting freedom of expression for all artists, regardless of creed or nation."
"I would also like to publicly dissociate myself with those Scottish a rts figures calling for artistic censorship."
The director of the company, Arik Eshet, said he was "comforted" to hear Ms Hyslop's words but saddened by the letter, although he said he still intends to bring his company to Edinburgh.
"It is a question of freedom of speech and it is mystifying for me that people who believe in dialogue and dignity want a boycott," he said. "We are not agents of the government of Israel. Yes, we do receive funds from them, although only in the last two years. We started in pubs making satire and it was usually at the expense of the establishment, and we get support from them even though we are not politically correct."
Mr Eshet, is a former board member of Waah-at i-sal-aam/Neve shalom, a community school jointly established by Jewish and Palestinian citizens of Israel.
Incubator Theatre is also funded by the Beracha Foundation, which seeks to promote Jewish-Arab coexistence.
Mr Eshet added: "The signatories to this letter are seeing us in black and white. I am against the violence and against the occupation. I am a progressive. But I am also a citizen who wants safety and is against terrorism.
"The thing that frightens me is extremities - I would meet anyone to have dialogue. They have a right to boycott the play if that is their opinion, but it is not a political play."
John Stalker Productions is promoting the show.
Mr Stalker said: "I recognise the right of those who support a boycott of Israeli goods and services to hold this view.
"Nevertheless, I do not support any attempt to restrict artistic freedom of expression or debate and support the right of the actors in the city to perform in Edinburgh this August, however difficult this view may be for some to accept given the terrible situation occurring now in Gaza and Israel."