The surreal and complex movie by director Samuel Maoz includes what could be seen as a critical view of the Israeli military.
It also won the Grand Jury prize at this month's Venice Film Festival, but Regev, who has frequently criticised Israel's cultural elite, is not a fan -- though she reportedly said at the time of the Venice festival that she had not seen it.
After having walked out last year, she was not invited to this year's Ophir Awards -- Israel's version of the Oscars -- last evening.
She referred to a striking scene in the film and called it a "blood libel."
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"As a minister and mother who has served in the Israeli army, I am ashamed that such a film has won such a prestigious prize," she posted on Facebook after the award was given.
An allegation from the Middle Ages -- that Jews murdered Christian children to use their blood for ritual purposes -- gave rise to the term "blood libel".
Academy director Mosh Danon said: "Criticism is meant to strengthen and support.
"There is no us and you. There are no enemies. There is only a strong desire to fix and improve, together with the establishment."
Winning best picture at the Ophir Awards makes the film eligible for inclusion in the foreign-language category at the Oscars, or Academy Awards, in the US.
Regev, who belongs to what is seen as Israel's most right-wing government ever, has repeatedly taken on the country's largely left-wing Jewish cultural elite.
They have accused her of seeking to muzzle them, including by promoting a bill to cut subsidies to cultural institutions deemed not "loyal" to the state.
"As the famous Chinese philosopher Sun Tzu once said: 'Cut the bullshit,'" she said.