Israel said it had made a formal protest to the Romanian government.
"They were dragged out of the car, even though they showed their passports and explained they had nothing" to do with the protest, the embassy said, according to AP.
There was no immediate response from the Romanian police, but President Klaus Iohannis condemned the violence, saying "the brutal repression of demonstrators is totally unacceptable."
"In a European state, attacking innocent people, attacking journalists, attacking women and children is inconceivable," he said in a statement on Monday that called for an investigation.
Marco Maximilian Katz, an Israeli and Romanian national who lives in Bucharest, said the police's actions had been "disgraceful".
“It is also scandalous that the police refused to take a look at the passports presented to them by the tourists who had nothing to do with the demonstrations. This should not happen in a EU member state,” he said.
Many Israelis have ancestral roots in Romania and some of them have taken advantage of the country’s nationality law, which allows them to reclaim Romanian citizenship of which they or their family were deprived when emigrating to Israel.
At 800,000, Romania boasted one of the largest pre-war Jewish communities in Europe. Around half survived the Holocaust and most made aliyah after 1945.