The director of the controversial production of “Julius Caesar” in Central Park and his family have received death threats at their Brooklyn home, his daughter told The Post.

“It’s sexual attacks on my mother — ‘grab her by the p—y,’ raping her — threats on me, and physical threats on my father’s life,” said Kyle Brown, 26, the daughter of Public Theater artistic director Oskar Eustis.

“It’s not okay. It’s stuff we did not sign up for — nothing that the show justified.”

“Your husband wants Trump to die. I want him to die,” stated one message left, according to police.

The caller rang their Brooklyn apartment eight or nine times in a half-hour and called back several times the next day, prompting the family to alert police, Brown said. He also threatened to publish their home address and phone number, she said.

Brown has been temporarily staying with her parents, and the caller seemed to know she was there despite there being no public record of it, which was particularly alarming, she said.

“The fact that he knew I lived at home was a very specific thing that triggered my parents,” she said. “My family’s been through so much.”

Eustis is the artistic director of the Public Theater and has been directing Shakespeare in the Park’s production of the classic, which has drawn fire for depicting Caesar — who is brutally murdered by Roman senators in the play’s third act — as President Trump.

The production has been interrupted by protesters three times — first by an alt-right blogger who hopped up on stage and berated the crowd on June 16 while a fellow right-wing writer livestreamed the off-script moment from the audience and shouted that theater-goers were “Nazis.”

Two more protesters stormed the stage at different points in the play’s final, June 18 staging, with one shouting, “Liberal hate kills!”

Critics including the president’s son Donald Jr. have blamed the production, which depicts a Trump-like Caesar being stabbed in the play’s most famous scene, for encouraging violence against conservative politicians, and particularly for the shooting of Rep. Steve Scalise and congressional staffers by a left-wing lunatic in Washington, DC, on June 14.

Delta Air Lines, American Express and Bank of America pulled their sponsorships of the Public Theater in response to the controversy.

The backlash prompted Eustis to post an open letter to the theater’s website defending the production.

The Public Theater did not immediately respond to requests for comment.