Barenboim was promoting a book he wrote with Palestinian intellectual Edward Said and refused to let Army radio reporter Dafna Arad interview him because she was wearing a military uniform, the BBC reported Saturday.
Arad said Barenboim told her he would grant the interview if she came back in civilian clothing.
Education Minister Limor Livnat said the incident shows Barenboim is "a real Jew-hater, a real anti-Semite."
Barenboim, a native of Argentina, has come under fire in Israel in the past for criticizing the occupation of the West Bank and Gaza.
He caused controversy in 2001 by performing the works of Richard Wagner, whose music had been appropriated by the Nazis after his death.